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Vertex partitions of chordal graphs
Author(s) -
Wood David R.
Publication year - 2006
Publication title -
journal of graph theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 54
eISSN - 1097-0118
pISSN - 0364-9024
DOI - 10.1002/jgt.20183
Subject(s) - combinatorics , mathematics , chordal graph , vertex (graph theory) , partition (number theory) , block graph , discrete mathematics , trémaux tree , graph , pathwidth , 1 planar graph , line graph
A k‐tree is a chordal graph with no ( k + 2)‐clique. An ℓ‐ tree‐partition of a graph G is a vertex partition of G into ‘bags,’ such that contracting 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 each bag induces a connected ${\lfloor k} /(\ell+1) \rfloor$ ‐tree. An analogous result is proved for oriented k ‐trees. © 2006 Wiley Periodicals, Inc. J Graph Theory 53: 167–172, 2006