### Jeong Ok Choi (최정옥), Various game-theoretic models on graphs

Room B232 IBS (기초과학연구원)

We introduce some of well-known game-theoretic graph models and related problems. A contagion game model explains how an innovation diffuses over a given network structure and focuses on finding conditions on which structure an innovation becomes epidemic. Regular infinite graphs are interesting examples to explore. We show that regular infinite trees make an innovation least

### Jaeseong Oh (오재성), A 2-isomorphism theorem for delta-matroids

Room B232 IBS (기초과학연구원)

Whitney’s 2-Isomorphism Theorem characterises when two graphs have isomorphic cycle matroids. In this talk, we present an analogue of this theorem for graphs embedded in surfaces by characterising when two graphs in surface have isomorphic delta-matroids. This is based on the joint work with Iain Moffatt.

### Daniel Cranston, Vertex Partitions into an Independent Set and a Forest with Each Component Small

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For each integer $k\ge 2$, we determine a sharp bound on $\operatorname{mad}(G)$ such that $V(G)$ can be partitioned into sets $I$ and $F_k$, where $I$ is an independent set and $G$ is a forest in which each component has at most k vertices. For each $k$ we construct an infinite family of examples showing our result is best

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T.B.A.

### Yijia Chen (陈翌佳), Graphs of bounded shrub-depth, through a logic lens

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Shrub-depth is a graph invariant often considered as an extension of tree-depth to dense graphs. In this talk I will explain our recent proofs of two results about graphs of bounded shrub-depth. Every graph property definable in monadic-second order logic, e.g., 3-colorability, can be evaluated by Boolean circuits of constant depth and polynomial size, whose

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### Karl Heuer, TBA

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기초과학연구원 수리및계산과학연구단 이산수학그룹
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