기초과학연구원 이산수학그룹
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In the "cake partition" problem n players have each a list of preferred parts for any partition of the interval ("cake") into n sub-intervals. Woodall, Stromquist and Gale proved independently that under mild conditions on the list of preferences (like continuity) there is always a partition and assignment of parts to the players, in which every player gets … |
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We prove a conjecture of Boros, Caro, Furedi and Yuster on the maximum number of edges in a 2-connected graph without repeated cycle lengths, which is a restricted version of a longstanding problem of Erdos. Our proof together with the matched lower bound construction of Boros, Caro, Furedi and Yuster show that this problem can … |
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This talk considers the following question at the intersection of extremal and structural graph theory: What is the maximum number of copies of a fixed forest $T$ in an $n$-vertex graph in a graph class $\mathcal{G}$ as $n\to \infty$? I will answer this question for a variety of sparse graph classes $\mathcal{G}$. In particular, we show that the answer is … |
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