Induced Subgraphs of Bounded Degree and Bounded Treewidth [chapter]

Prosenjit Bose, Vida Dujmović, David R. Wood
2005 Lecture Notes in Computer Science  
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
more » ... 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.
doi:10.1007/11604686_16 fatcat:otychvzqsnftbp7n2aanmd7j2a