Boram Park (박보람), Odd coloring of sparse graphs

Room B232 IBS (기초과학연구원)

We introduce an odd coloring of a graph, which was introduced very recently, motivated by parity type colorings of graphs. A proper vertex coloring of graph $G$ is said to be odd if for each non-isolated vertex $x \in V (G)$ there exists a color $c$ such that $c$ is used an odd number of

Cheolwon Heo (허철원), The complexity of the matroid-homomorphism problems

Room B332 IBS (기초과학연구원)

In this talk, we introduce homomorphisms between binary matroids that generalize graph homomorphisms. For a binary matroid $N$, we prove a complexity dichotomy for the problem $\rm{Hom}_\mathbb{M}(N)$ of deciding if a binary matroid $M$ admits a homomorphism to $N$. The problem is polynomial-time solvable if $N$ has a loop or has no circuits of odd

Kyeongsik Nam (남경식), Large deviations for subgraph counts in random graphs

Room B332 IBS (기초과학연구원)

The upper tail problem for subgraph counts in the Erdos-Renyi graph, introduced by Janson-Ruciński, has attracted a lot of attention. There is a class of Gibbs measures associated with subgraph counts, called exponential random graph model (ERGM). Despite its importance, lots of fundamental questions have remained unanswered owing to the lack of exact solvability. In

Andreas Holmsen, A colorful version of the Goodman-Pollack-Wenger transversal theorem

Room B332 IBS (기초과학연구원)

Hadwiger's transversal theorem gives necessary and sufficient conditions for the existence of a line transversal to a family of pairwise disjoint convex sets in the plane. These conditions were subsequently generalized to hyperplane transversals in $\mathbb{R}^d$ by Goodman, Pollack, and Wenger. Here we establish a colorful extension of their theorem, which proves a conjecture of

Jan Kurkofka, Canonical Graph Decompositions via Coverings

Zoom ID: 869 4632 6610 (ibsdimag)

We present a canonical way to decompose finite graphs into highly connected local parts. The decomposition depends only on an integer parameter whose choice sets the intended degree of locality. The global structure of the graph, as determined by the relative position of these parts, is described by a coarser model. This is a simpler

Gil Kalai, The Cascade Conjecture and other Helly-type Problems

Zoom ID: 868 7549 9085

For a set $X$ of points $x(1)$, $x(2)$, $\ldots$, $x(n)$ in some real vector space $V$ we denote by $T(X,r)$ the set of points in $X$ that belong to the convex hulls of r pairwise disjoint subsets of $X$. We let $t(X,r)=1+\dim(T(X,r))$. Radon's theorem asserts that If $t(X,1)< |X|$, then $t(X, 2) >0$. The first

Stijn Cambie, The precise diameter of reconfiguration graphs

Room B332 IBS (기초과학연구원)

Reconfiguration is about changing instances in small steps. For example, one can perform certain moves on a Rubik's cube, each of them changing its configuration a bit. In this case, in at most 20 steps, one can end up with the preferred result. One could construct a graph with as nodes the possible configurations of

Sebastian Siebertz, Transducing paths in graph classes with unbounded shrubdepth

Zoom ID: 869 4632 6610 (ibsdimag)

Transductions are a general formalism for expressing transformations of graphs (and more generally, of relational structures) in logic. We prove that a graph class C can be FO-transduced from a class of bounded-height trees (that is, has bounded shrubdepth) if, and only if, from C one cannot FO-transduce the class of all paths. This establishes

KSIAM 2022 Spring Meeting

IBS Science Culture Center

KSIAM (Korean Society for Industrial and Applied Mathematics) will have the KSIAM 2022 Spring Conference at the Institute for Basic Science (IBS). Its academic session for Combinatorics decided to have an invited talk by Joonkyung Lee at the Hanyang University, a special session "Graph Theory" organized by Sang-il Oum and the IBS DIMAG, a special session "Enumerative Combinatorics"

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