Induced subgraphs of bounded degree and bounded treewidth

Prosenjit Bose, Vida Dujmovic, David R. Wood

Research output: Contribution to journalArticleResearchpeer-review


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.
Original languageEnglish
Pages (from-to)88-105
Number of pages18
JournalContributions to Discrete Mathematics
Issue number1
Publication statusPublished - 2006
Externally publishedYes

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