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2005
Springer

Induced Subgraphs of Bounded Degree and Bounded Treewidth

10 years 3 months ago
Induced Subgraphs of Bounded Degree and Bounded Treewidth
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.
Prosenjit Bose, Vida Dujmovic, David R. Wood
Added 28 Jun 2010
Updated 28 Jun 2010
Type Conference
Year 2005
Where WG
Authors Prosenjit Bose, Vida Dujmovic, David R. Wood
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