Reduced clique graphs of chordal graphs

Authors:
Michel Habib;Juraj Stacho
Affiliations:
LIAFA-CNRS and Université Paris Diderot-Paris VII, Case 7014, 75205 Paris Cedex 13, France;Wilfrid Laurier University, Department of Physics & Computer Science, 75University Ave W, Waterloo, ON N2L 3C5, Canada
Venue:
European Journal of Combinatorics
Year:
2012

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Abstract

We investigate the properties of chordal graphs that follow from the well-known fact that chordal graphs admit tree representations. In particular, we study the structure of reduced clique graphs which are graphs that canonically capture all tree representations of chordal graphs. We propose a novel decomposition of reduced clique graphs based on two operations: edge contraction and removal of the edges of a split. Based on this decomposition, we characterize asteroidal sets in chordal graphs, and discuss chordal graphs that admit a tree representation with a small number of leaves.