기초과학연구원 이산수학그룹
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Let $\mathcal{F}$ be a family of graphs, and let $p$ and $r$ be nonnegative integers. The $(p,r,\mathcal{F})$-Covering problem asks whether for a graph $G$ and an integer $k$, there exists a set $D$ of at most $k$ vertices in $G$ such that $G^p\setminus N_G^r$ has no induced subgraph isomorphic to a graph in $\mathcal{F}$, where … |
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By a seminal result of Valiant, computing the permanent of (0, 1)-matrices is, in general, #P-hard. In 1913 Pólya asked for which (0, 1)-matrices A it is possible to change some signs such that the permanent of A equals the determinant of the resulting matrix. In 1975, Little showed these matrices to be exactly the … |
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A linear $3$-graph is called a (3-)hypertree if there exists exactly one path between each pair of two distinct vertices. A linear $3$-graph is called a Steiner triple system if each pair of two distinct vertices belong to a unique edge. A simple greedy algorithm shows that every $n$-vertex Steiner triple system $G$ contains all … |
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