기초과학연구원 이산수학그룹
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Given a graph $G$, a decomposition of $G$ is a collection of spanning subgraphs $H_1, \ldots, H_t$ of $G$ such that each edge of $G$ is an edge of $H_i$ for exactly one $i \in \{1, \ldots, t\}$. Given a positive integer $d$, a graph is said to be $d$-degenerate if every subgraph of it has … |
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Integer programming is the problem of optimizing a linear function over the set of integer solutions satisfying a system of inequalities. The most successful technique in practice is the so-called "cutting-plane" algorithm in combination with branch-and-bound enumeration. Cutting-planes for an integer linear program are linear inequalities that are valid for all integer feasible solutions but … |
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Our problem can be described in terms of a two player game, played with the set $\mathcal{S}_n$ of permutations on $\{1,2,\dots,n\}$. First, Player 1 selects a subset $S$ of $\mathcal{S}_n$ and shows it to Player 2. Next, Player 2 selects a permutation $p$ from $\mathcal{S}_n$ as different as possible from the permutations in $S$, and shows it to Player … |
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The strong clique number of a graph $G$ is the maximum size of a set of edges of which every pair has distance at most two. In this talk, we prove that every $\{C_5,C_{2k}\}$-free graph has strong clique number at most $k\Delta(G)-(k-1)$, which resolves a conjecture by Cames van Batenburg et al. We also prove … |
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