기초과학연구원 이산수학그룹
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The Caccetta-Haggkvist conjecture, one of the best known in graph theory, is that in a digraph with $n$ vertices in which all outdegrees are at least $n/k$ there is a directed cycle of length at most $k$. This is known for large values of $k$, relatively to n, and asymptotically for n large. A few … |
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Graph Minor project by Robertson and Seymour is perhaps the deepest theory in Graph Theory. It gives a deep structural characterization of graphs without any graph $H$ as a minor. It also gives many exciting algorithmic consequences. In this work, I would like to talk about our attempt to extend Graph minor project to directed … |
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Our talk will mainly focus on the relationship between substructures and eigenvalues of graphs. We will briefly survey recent developments on a conjecture of Bollobás and Nikiforov and a classical result of Nosal on triangles. In particular, we shall present counting results for previous spectral theorems on triangles and quadrilaterals. If time allows, we will … |
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