Schedule

Day 1 — Tuesday, October 20, 2026

Time	Speaker	Title / Event
13:50-14:00	Opening Remark
14:00-14:50    Plenary Session좌장: 최일규
14:00-14:50	Alexandr V. Kostochka University of Illinois at Urbana–Champaign	DP vertex-arboricity of sparse graphs [PL] The vertex arboricity, $va(G)$, of a multigraph $G$ is the minimum number $k$ for which the vertex set of $G$ can be partitioned into $k$ subsets, each of which induces a graph with no cycles. By definition, if $va(G)=k$, then the chromatic number, $\chi(G)$, satisfies $k\leq \chi(G)\leq 2k$. Cornerstone results of Borodin in 1976 and of Bollobás and Manvel in 1979 on a more general topic yield an analog for vertex arboricity of the Gallai's lower bound on the number of edges in a $(2k-1)$-critical graph. In this talk we consider the DP-version of vertex arboricity. Introducing a slight generalization of this notion, we derive lower bounds on the number of edges in graphs critical with respect to DP vertex arboricity better than Gallai's bound. The proof yields similar bounds on the number of edges in graphs critical w.r.t. vertex arboricity and w.r.t. list arboricity. This is joint work with P. Bradshaw and Z. Xiang.
14:50-15:10	Break
15:10-16:25    Contributed Session 1좌장: 이상준
15:10-15:35	Seog-Jin Kim Konkuk University	The Alon-Tarsi number of squares of subcubic planar graphs without cycles of lengths $4$ to $8$ [CT] The Alon-Tarsi number $AT(G)$ of a graph $G$, defined via the graph polynomial, is a strengthening of the list chromatic number $\chi_{\ell}(G)$. We study the Alon-Tarsi number of squares of planar graphs. The square of a graph $G$ is the graph obtained by joining every pair of vertices whose distance in $G$ is at most $2$. Recently, Kim and Luo (2026) proved that $\chi_{\ell}(G^2)\le 6$ for every subcubic planar graph containing no $k$-cycles for $4\le k\le 8$. We strengthen this result by proving that $AT(G^2)\le 6$ for every such graph $G$. This is joint work with Xiaopan Lian (Nankai University) and Rong Luo (West Virginia University).
15:35-16:00	Jaehyeon Seo Yonsei University	Fractional colorings of $K_r$-free graphs with local demands [CT] We study fractional colorings of $K_r$-free graphs with vertex-dependent demands. A $\phi$-coloring is a probability distribution on independent sets such that each vertex $v$ is included with probability at least $\phi(v)$. We prove that, for every integer $r\ge 4$, there exist constants $c_r>0$ and $\delta_0$ such that every $K_r$-free graph $G$ with minimum degree at least $\delta_0$ admits a $\phi$-coloring whenever $\phi(v)\le c_r\frac{\log \deg(v)}{\deg(v)\log\log \deg(v)}$ for every vertex $v$. The bound has the same order as the fractional consequence of Johansson's theorem, but with the maximum degree replaced locally by $\deg(v)$. Our proof uses a randomized independent-set algorithm based on an entropy method introduced by Dhawan. Its main additional ingredient is a system of modifier variables adapted from Bansal, Gupta, and Guruganesh's treatment of Johansson's method. This is joint work with Huy Nguyen (University of Illinois Urbana–Champaign), David Gallardo (University of Illinois Urbana–Champaign), Abhishek Methuku (University of Illinois Urbana–Champaign), Ewan Davies (Colorado State University), Abhishek Dhawan (University of Illinois Urbana–Champaign), and Samuel Spiro (Georgia State University).
16:00-16:25	Seokbeom Kim KAIST & IBS DIMAG	On the chromatic number of the union of comparability graphs [CT] Resolving in a strong sense a problem of Gyárfás on the union of two perfect graphs, we prove that for every pair of positive integers $d$ and $k$, there is a graph $G$ with clique number $k$ and chromatic number $k^d$ that is the union of $d$ comparability graphs. We also show that the chromatic number can be replaced by the fractional chromatic number or $\frac{|V(G)|}{\alpha(G)}$. This talk is based on a joint work with Wouter Cames van Batenburg (Université libre de Bruxelles), Maria Chudnovsky (Princeton University), Linda Cook (University of Utrecht), James Davies (Leipzig University), and Sang-il Oum (IBS Discrete Mathematics Group).
16:25-17:10	Check-in
17:10-18:00    Invited Session 1좌장: 김석진
17:10-18:00	Jakub Przybyło AGH University of Krakow	How Far Is Arboricity from Degeneracy? [IT] Arboricity and degeneracy are two classical and closely related measures of graph sparsity. Although their definitions reflect rather different structural properties, the two parameters are tied together by well-known inequalities, which naturally raise the question of how close the corresponding classes of sparse graphs actually are. In this talk, we investigate this question from a decomposition perspective. We show that graphs of bounded arboricity can be made substantially closer to having the corresponding degeneracy by separating off a graph of suitably bounded degree. More generally, we discuss which combinations of degeneracy and maximum-degree bounds can be guaranteed in such decompositions. Our results provide essentially sharp answers to these questions and are constructive in nature.
18:00-	Dinner

Day 2 — Wednesday, October 21, 2026

Time	Speaker	Title / Event
09:00-09:50    Invited Session 2좌장: Mark Siggers
09:00-09:50	Cheolwon Heo SUNY Korea	Dismantlability in Matroid Homomorphism Reconfiguration [IT] A matroid homomorphism from a binary matroid $M$ to a binary matroid $N$ is a map $\phi:E(M)\to E(N)$ such that, for every circuit $C$ of $M$, the set of elements of $N$ that occur an odd number of times among $\phi(e)$, $e\in C$, is a disjoint union of circuits of $N$. This notion generalizes graph homomorphisms: if $f:G\to H$ is a graph homomorphism, then the induced map on edges, defined by $\phi(uv)=f(u)f(v)$, is a matroid homomorphism from the graphic matroid $M(G)$ to $M(H)$. Reconfiguration problems for graph homomorphisms, in which one transforms one homomorphism into another through a sequence of local changes, have been extensively studied. A result of Brightwell and Winkler shows that a graph $H$ has the property that, for every graph $G$, any two homomorphisms from $G$ to $H$ can be connected by such a reconfiguration sequence if and only if $H$ is dismantlable to a single vertex. In this talk, we introduce a reconfiguration framework for matroid homomorphisms and establish a matroidal analogue of the Brightwell–Winkler theorem.
09:50-10:10	Break
10:10-11:00    Contributed Session 2좌장: 권영수
10:10-10:35	Donggyu Kim Hanyang University	On the enumeration of polymatroids [CT] Let $p_k(n)$ be the number of $k$-polymatroids on $[n]$. We show that for every fixed $k \geq 1$, we have \[\left\lfloor \frac{k}{2} \right\rfloor \cdot \binom{n}{\lfloor n/2 \rfloor} \cdot (1+o(1)) \le \log_2 p_k(n) \le k \cdot \binom{n}{\lfloor n/2 \rfloor} \cdot (1+o(1)).\] We also show that for $k \geq 2$, almost all $k$-polymatroids are (i) connected, (ii) proper, and (iii) not linearly representable over any field. This is joint work with Seonghyuk Im (KIAS).
10:35-11:00	Denys Bulavka Dalhousie University	Maximal matroids and counterexamples [CT] Given a pattern graph $P$, a subgraph $G$ of the complete graph $K_n$ is weakly $P$-saturated if one can add all the missing edges from $G$ to itself in order, at each step creating a copy of $P$ that uses the newly added edge. The minimum size of such a graph $G$ is known as the weakly $P$-saturation number (of $K_n$). One strategy to provide a lower bound for the weak $P$-saturation number is by exhibiting a matroid having $P$ as a circuit, then its rank provides such a lower bound. Thus, maximal matroids for a prescribed set of circuits are of interest. Two matroids have been widely used for determining the weak saturation number for cliques and complete bipartite graphs: the rigidity and the hyperconnectivity matroid. Jackson and Tanigawa conjectured that the $d$-rigidity matroid and the $d$-hyperconnectivity matroid are the unique maximal matroids in the posets of matroids having $\{K_{d+2},K_{d+2,d+2}\}$ as circuits, and matroids having $\{K_{d+2},K_{d+1,d+1}\}$ as circuits, respectively. We disprove these conjectures by showing the existence of maximal matroids that are distinct from the proposed candidates. This is a joint work with Martin Tancer (Charles University).
11:00-11:10	Short break
11:10-12:00    Invited Session 3좌장: 권오정
11:10-12:00	Tony Huynh IBS DIMAG	Rigidity Theory for Combinatorialists [IT] Rigidity theory is a subject with a rich mathematical history dating at least back to the work of Cauchy and Euler on the rigidity of 3-dimensional polytopes. I will begin with a gentle introduction to the topic and explain how central questions in rigidity theory give rise to intriguing combinatorial problems. For example, I will describe connections between rigidity theory and graph connectivity, edge-colourings, random thresholds, surface triangulations, treewidth, and the theory of graph minors. Disclaimer: I am not a rigidity theorist.
12:00-14:00	Lunch
14:00-14:50    Invited Session 4좌장: 안정호
14:00-14:50	Dabeen Lee Seoul National University	Learning while scheduling: contextual queueing bandits [IT] How should jobs be scheduled when their service rates are not known in advance? In this talk, we study this question through contextual queueing bandits, where jobs have heterogeneous features and a scheduler must learn unknown service rates while deciding which job to process and which server to use. A central challenge is that each scheduling decision changes the queue, shaping the choices available in the future. We discuss how to integrate online learning with scheduling to balance exploration and efficient service, and present queue-length guarantees relative to a scheduler that knows the service rates. The talk highlights the interplay between learning from partial feedback, resource allocation, and congestion control. This talk is based on joint work with Seoungbin Bae and Garyeong Kang.
14:50-15:10	Break
15:10-16:25    Contributed Session 3좌장: 박종육
15:10-15:35	Julien Codsi Princeton University	Between the Grid Minor Theorem and the Pathwidth Theorem [CT] One way to interpret the grid minor theorem is the following: forbidding a planar graph that is minor-universal for all planar graphs up to a given size forces the treewidth to be bounded. Similarly, the pathwidth theorem tells us that forbidding a tree that is minor-universal for all trees up to a given size forces the pathwidth to be bounded. From this perspective, it is natural to ask what happens between these two. What can we say if we forbid a minor-universal outerplanar graph? What about a minor-universal series-parallel graph? In this talk, I will present some partial answers to these questions, filling part of the gap between trees and planar graphs.
15:35-16:00	Mujin Choi KAIST & IBS DIMAG	Odd-Cycle-Packing-treewidth and Grid Theorem for odd-minor relation [CT] We introduce a new graph parameter Odd-Cycle-Packing-treewidth (OCP-tw), which decomposes a given graph into parts of bounded odd cycle packing number. We then establish an analogue to the celebrated Grid Theorem of Robertson and Seymour for OCP-tw. Specifically, we identify two infinite families of grid-like graphs whose presence as odd-minors implies large OCP-tw and excluding them as an odd-minor implies bounded OCP-tw. This structural result is constructive and implies a $2^{\mathbf{poly}(k)}\mathbf{poly}(n)$-time parameterized $\mathbf{poly}(k)$-approximation algorithm for OCP-tw. Moreover, we show that the (weighted) Maximum Independent Set problem (MIS) can be solved in polynomial time on graphs of bounded OCP-tw. This is joint work with Gunwoo Kim (KAIST / IBS DIMAG), Caleb McFarland (Georgia Institute of Technology), Maximilian Gorsky (IBS DIMAG), and Sebastian Wiederrecht (IBS DIMAG).
16:00-16:25	Hojin Chu KIAS	Minimum degree conditions for removable matchings in $k$-connected graphs [CT] In 1969, Halin proved that every $k$-connected graph $G$ with minimum degree at least $k+1$ contains an edge $e$ such that $G-e$ is $k$-connected. As an edge is a matching of size one, it is natural to ask whether Halin's result extends to matchings of larger size, a question recently investigated by Li, Zhou, Fujita, and Mao. A matching $M$ of a $k$-connected graph $G$ is called $k$-removable if $G-M$ is $k$-connected. In this paper, we verified a conjecture of Li, Zhou, Fujita, and Mao in the range $\delta(G)\ge2k+1$ as follows: every $k$-connected graph $G$ with $\delta(G)\ge2k+1$ contains a $k$-removable matching of size $\bigl\lceil(\delta(G)+1)/2\bigr\rceil$, unless $\delta(G)$ is even and $G\cong K_{\delta(G)+1}$. Our main tool, of independent interest, is a strengthening of Halin's result producing a $k$-removable edge that avoids a prescribed set of vertices. This is joint work with Ringi Kim (Inha University) and Boram Park (Seoul National University).
16:25-16:45	Break
16:45-17:35    Contributed Session 4좌장: 신희성
16:45-17:10	Hyemin Kwon Seoul National University	Det-extremal cubic graphs and the total domatic number [CT] A graph $G$ is det-extremal if $|\det A|=\operatorname{per} A$ for its adjacency matrix $A$. Det-extremal cubic bipartite graphs arise in the study of Pólya's permanent problem. The total domatic number of a graph is the largest number of pairwise disjoint total dominating sets. Characterization of the cubic graphs with total domatic number $1$ has been a long-standing open problem. In this talk, we discuss a connection between det-extremal cubic graphs and the total domatic number. In particular, we show that a connected cubic graph is det-extremal if and only if its total domatic number is $1$. We also present structural results on det-extremal cubic graphs, including extensions of known characterizations and bounds on their girth and order. These results, in turn, provide new insights into cubic graphs with total domatic number $1$. This is joint work with Myungho Choi (Kyunggi High School) and Boram Park (Seoul National University).
17:10-17:35	Jiadong Wu Shanghai University / SUNY	Unique spectral extremal graphs for complete multipartite edge-color-critical subgraphs [CT] A graph is non-$r$-partite if its chromatic number exceeds $r$. For a graph $F$ with $\chi(F)=r+1$, let $\mathrm{ex}_{r+1}(n,F)$ and $\mathrm{ex}_{r+1,\rho}(n,F)$ denote the maximum number of edges and the maximum adjacency spectral radius among non-$r$-partite $F$-free graphs of order $n$, and let $\mathrm{EX}_{r+1}(n,F)$ and $\mathrm{EX}_{r+1,\rho}(n,F)$ be the corresponding families of extremal graphs. Fang and Lin conjectured that $\mathrm{EX}_{r+1,\rho}(n,F)\subseteq\mathrm{EX}_{r+1}(n,F)$ for every edge-color-critical $F$ and all large $n$. A complete multipartite graph with chromatic number $r+1$ is edge-color-critical exactly when it has at least two singleton parts. We confirm the conjecture for all such graphs, in each case in the stronger form of a unique spectral extremal graph, which we determine explicitly. We prove a reduction principle: if $F$ is edge-color-critical, satisfies a local embedding condition, and has $\mathrm{ex}_{r+1}(n,F)=|E(T_{n,r})|-\lfloor n/r\rfloor+2(s-1)$ for the associated threshold $s\ge2$, then for all large $n$ every spectral extremal graph is edge extremal and, moreover, is unique. The conclusion is stronger than the conjectured inclusion, and the difference is not vacuous: we exhibit forbidden graphs for which $\mathrm{EX}_{r+1}(n,F)$ has several members while $\mathrm{EX}_{r+1,\rho}(n,F)$ has exactly one. The comparison that decides the extremal configuration takes place at the scale $\Theta(1/n)$, where a first-order Rayleigh estimate is inconclusive, and two devices are used there: a direct comparison of the secular functions of an explicit low-dimensional family of graphs, and a second-order residual refinement of the Rayleigh principle of Temple type. We then carry out the required edge count. For $F=K_{1,1,t_3,\ldots,t_{r+1}}$ with all $t_i\ge2$ and $t_{\min}=\min\{t_3,\ldots,t_{r+1}\}$, the unique spectral extremal graph is obtained from a complete $r$-partite graph of order $n-1$ with parts balanced to within one vertex by adding a vertex joined to all of the $r-2$ largest parts and to exactly $t_{\min}-1$ vertices of each of the other two. The remaining case $F=K_{1,1,1,t_4,\ldots,t_{r+1}}$ lies outside the embedding framework and is settled by a different mechanism: for $r\ge3$ the unique spectral extremal graph is $Y_r(n)$, and we determine the corresponding edge extremal number as well, extending a theorem of Brouwer from $K_{r+1}$ to this family. All arguments are self-contained. This is joint work with Suil O (SUNY Korea).
18:00-	Dinner

Day 3 — Thursday, October 22, 2026

Time	Speaker	Title / Event
09:00-09:50    Invited Session 5좌장: 서승현
09:00-09:50	Jongbaek Song Pusan National University	Polytopes, face numbers and toric varieties [IT] The g-conjecture, proved by Billera and Lee (1981) and Stanley (1980), gives a comprehensive combinatorial characterization of simplicial (or simple) polytopes in terms of their face numbers. Stanley's contribution to this conjecture employed toric geometry, specifically leveraging the connection between the face numbers of lattice polytopes and a certain topological invariant of (rationally) smooth toric varieties. In this talk, I will outline the key ideas behind this connection and discuss possible extensions to more general lattice polytopes and corresponding singular toric varieties. This talk is based on the joint work with Seonjeong Park (Jeonju University).
09:50-10:10	Break
10:10-12:00    Contributed Session 5좌장: 남하얀
10:10-10:35	Daniel McGinnis IBS Discrete Mathematics Group	Multi-graded generic initial ideals, regularity, and the optimal colorful fractional Helly theorem for $d$-Leray complexes [CT] A celebrated result of Bayer and Stillman from 1987 states that for a homogeneous ideal $I$ of a polynomial ring $S$, the regularities of $S/I$ and $S/\textrm{GIN}(I)$ are the same under the reverse lexicographic monomial ordering, where $\textrm{GIN}(I)$ is the generic initial ideal. If $R$ is a polynomial ring whose variables are subdivided into disjoint blocks of variables $X_1,\dots,X_c$, there is a natural multi-grading on $R$, and one can analogously define a multi-graded version of the generic initial ideal for any multi-homogeneous ideal $I$ of $R$. However, the full strength of the Bayer–Stillman Theorem fails in the multi-graded setting; there are multi-homogeneous ideals $I$ such that the regularities are not preserved after passing to the multi-graded generic initial ideal no matter the choice of monomial ordering. We prove lower bounds on the regularity of $R/I$ in terms of almost regular sequences of the multi-graded generic initial ideal of $I$ restricted to each block of variables. Again, we use the reverse lexicographic monomial ordering, but interestingly, the lower bound result requires a particular choice of ordering on the variables. As an application, we prove the optimal fractional Helly theorem for $d$-Leray simplicial complexes, a problem stemming from the work of Kim in 2017.
10:35-11:00	Olga Medrano Martín del Campo IBS Discrete Mathematics Group	Local combinatorial analogues for bounded VC dimension [CT] Stable graphs, or equivalently Littlestone classes, were characterized by the existence of linear-sized `good' sets, a kind of strongly homogeneous set, in the work of Malliaris-Shelah and Malliaris-Moran. We prove a parallel result for classes of bounded VC dimension, showing that these are characterized by the existence of linear-sized symmetric or asymmetric good pairs (which we define). We give three proofs, each requiring drawing from methods and results from different areas, and resulting in different kinds of bounds.
11:00-11:10	Short break
11:10-11:35	Musung Kang Seoul National University	An exact obstruction to uniform average mixing on the paths $P_{12m-1}$ [CT] Continuous Time Quantum Walks on Graphs (CTQW) were proposed by Feynman, and rigorously invented by E. Farhi. C. D. Godsil and his research group members including K. Guo, G. Coutinho, and H. Zhan have developed the theory with algebraic/spectral graph theory, design theory (especially using Association Schemes) and analytic methods. They proposed a question about uniform average mixing matrix, whose probabilistic mixing are obtained from unistochastic matrix of CTQW, on such dynamics. [Baptista2024, Unexpected averages of mixing matrices]: Q. Which graph admits a uniform mixing under some sampling $R$; for path graphs, do all $P_n$ admit uniform average mixing $J/n$, where $J$ is the all-ones matrix? G. Coutinho and K. Guo posed an ambitious question. [Selected open problems in continuous-time quantum walks]: Q. How one can develop spectral graph theory for sampled mixing matrix? We answer the first question negative, and partially contribute to the second question.
11:35-12:00	Kyunghwan Song Jeju National University	$p$-numerical semigroup of the sequence of consecutive odd integers [CT] We introduce the proofs of the $p$-Frobenius problems proposed as Conjectures 7.1 and 7.5 developed by T. Komatsu and R. Pandey (Bull. Korean Math. Soc. 2025;62:1397–1409.) for two families of consecutive odd integers. For integers $r,L,n\ge0$, the bounded restricted partition function $p_{\le r}^{(\le L)}(\le n)$ counts partitions of $n$ into at most $r$ parts, each at most $L$. Thus the bounded restricted partition functions $p_{\le 3}^{(\le a)}(\le s)$ and $p_{\le 3}^{(\le a+1)}(\le s)$ play central roles in the proofs. Their generating functions are Gaussian polynomials, whose symmetry and unimodality provide a common tool for treating both families. This talk is based on the joint work with Takao Komatsu (Department of Mathematics, Institute of Science Tokyo; Jeju Glocal University Project of Jeju National University) and Sungjin Hyun (Jeju National University).
12:00-14:00	Lunch
14:00-	Free afternoon (Hwadam Botanic Garden recommended)

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