Algorithms in combinatorial geometry
Algorithms in combinatorial geometry
A partial k-arboretum of graphs with bounded treewidth
Theoretical Computer Science
Bounded-Degree Independent Sets in Planar Graphs
ISAAC '02 Proceedings of the 13th International Symposium on Algorithms and Computation
Linear-Time Reconstruction of Delaunay Triangulations with Applications
ESA '97 Proceedings of the 5th Annual European Symposium on Algorithms
Simultaneous diagonal flips in plane triangulations
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
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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.