기초과학연구원 이산수학그룹
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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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In this talk I will present a small result we achieved during a workshop in February this year. My coauthors on this are Marcin Pilipczuk, Paweł Komosa and Manuel Sorge. A bramble in an undirected graph $G$ is a family of connected subgraphs of $G$ such that for every two subgraphs $H_1$ and $H_2$ in the bramble either $V(H_1) \cap … |
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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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In extremal graph theory, a graph G is H-saturated if G does not contain a copy of H but adding any missing edge to G creates a copy of H. The saturation number, sat(n, H), is the minimum number of edges in an n-vertex H-saturated graph. This class of problems was first studied by Zykov … |
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The study of Hamiltonian graphs, i.e. finite graphs having a cycle that contains all vertices of the graph, is a central theme of finite graph theory. For infinite graphs such a definition cannot work, since cycles are finite. We shall debate possible concepts of Hamiltonicity for infinite graphs and eventually follow the topological approach by … |
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