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Induced Subgraphs of Bounded Degree and Bounded Treewidth (2008)
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@MISC{Bose08inducedsubgraphs,
author = {Prosenjit Bose and Vida Dujmović and David R. Wood},
title = { Induced Subgraphs of Bounded Degree and Bounded Treewidth },
year = {2008}
}
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Abstract
We prove that for all 0 ≤ t ≤ k and d ≥ 2k, every graph G with treewidth at most k has a ‘large ’ induced subgraph H, where H has treewidth at most t and every vertex in H has degree at most d in G. The order of H depends on t, k, d, and the order of G. With t = k, we obtain large sets of bounded degree vertices. With t = 0, we obtain large independent sets of bounded degree. In both these cases, our bounds on the order of H are tight. For bounded degree independent sets in trees, we characterise the extremal graphs. Finally, we prove that an interval graph with maximum clique size k has a maximum independent set in which every vertex has degree at most 2k.
