기초과학연구원 이산수학그룹
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Let $Q_n$ be the $n$-dimensional Hamming cube (hypercube) and $N=2^n$. We prove that the number of maximal independent sets in $Q_n$ is asymptotically $2n2^{N/4}$, as was conjectured by Ilinca and Kahn in connection with a question of Duffus, Frankl and Rödl. The value is a natural lower bound derived from a connection between maximal independent … |
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An odd $$-factor of a graph is a spanning subgraph $H$ such that for every vertex $v \in V(G)$, $1 \le d_H(v) \le b$, and $d_H(v)$ is odd. For positive integers $r \ge 3$ and $b \le r$, Lu, Wu, and Yang gave an upper bound for the third largest eigenvalue in an $r$-regular graph with even number of … |
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We discuss how the model theoretic notion of first-order transduction allows to define a notion of structural sparsity, and give some example of applications, like existence of low shrub-depth decompositions for tranductions of bounded expansion classes, characterization of transductions of classes with bounded pathwidth, decompositions of graphs with bounded rank-width into cographs. |
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