기초과학연구원 이산수학그룹
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The canonical tree-decomposition theorem, proved by Robertson and Seymour in their seminal graph minors series, turns out to be an extremely valuable tool in structural and algorithmic graph theory. In this paper, we prove the analogous result for digraphs, the directed tangle tree-decomposition theorem. More precisely, we introduce directed tangles and provide a directed tree-decomposition … |
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The notion of convexity spaces provides a purely combinatorial framework for certain problems in discrete geometry. In the last ten years, we have seen some progress on several open problems in the area, and in this talk, I will focus on the recent results relating to Tverberg’s theorem and the Alon-Kleitman (p,q) theorem. |
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We show that each perfect matching in a bipartite graph G intersects at least half of the perfect matchings in G. This result has equivalent formulations in terms of the permanent of the adjacency matrix of a graph, and in terms of derangements and permutations on graphs. We give several related results and open questions. This … |
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