Abstract
For a family F of graphs, a graph U is said to be F -induced-universal if every graph of F 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 ⌈ k / 2 ⌉ − 1 / k log 2 + 2 / k n ) vertices. This construction improves a result of Butler by a multiplicative constant factor for the even case and by almost a multiplicative n 1 / k factor for the 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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