# On induced-universal graphs for the class of bounded-degree graphs

Abstract : For a family $\cF$ of graphs, a graph $U$ is said to be $\cF$-induced-universal if every graph of $\cF$ is an induced subgraph of $U$. We give a construction for an induced-universal graph for the family of graphs on $n$ vertices with degree at most $k$. For $k$ even, our induced-universal graph has $O(n^{k/2})$ vertices and for $k$ odd it has $O(n^{\ceil{k/2}-1/k}\log^{2+2/k}n)$ vertices. This construction improves a result of Butler by a multiplicative constant factor for even case and by almost amultiplicative $n^{1/k}$ factor for odd case. We also construct induced-universal graphs for the class of oriented graphs with bounded incoming and outgoing degree, slightly improving another result of Butler.
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Journal articles

https://hal.archives-ouvertes.fr/hal-00368277
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Louis Esperet, Arnaud Labourel, Pascal Ochem. On induced-universal graphs for the class of bounded-degree graphs. Information Processing Letters, Elsevier, 2008, 108 (5), pp.255-260. ⟨10.1016/j.ipl.2008.04.020⟩. ⟨hal-00368277⟩

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