@MISC{Wood_vertexpartitions, author = {David R. Wood}, title = {VERTEX PARTITIONS OF CHORDAL GRAPHS}, year = {} }

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Abstract

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