Vertex partitions of chordal graphs

Abstract: A k-tree is a chordal graph with no (k + 2)-clique. An -treepartition of a graph G is a vertex partition of G into `bags,' such that contracting each bag to a single vertex gives an -tree (after deleting loops and replacing parallel edges by a single edge). We prove that for all k 0, every k-tree has an -tree-partition in which each bag induces a connected k/( + 1) -tree. An analogous result is proved for oriented k-trees.

• Type: Journal
• Year: 2006
• Where: JGT
• Authors: David R. Wood
• Keywords: Chordal Graph, JGT 2006, Single Vertex, Vertex Partition