On line perfect graphs

descriptionPublicationkeyboard_double_arrow_right Article 01 Dec 1978 English Publisher:Springer Science and Business Media LLCJournal:Mathematical Programming, volume 15, pages 236-238 (issn: 0025-5610, eissn: 1436-4646,

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Authors: Dominique de Werra;

doi: 10.1007/bf01609025

On line perfect graphs

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Abstract

Line-perfect graphs have been defined by L.E. Trotter as graphs whose line-graphs are perfect. They are characterized by the property of having no elementary odd cycle of size larger than 3. L.E. Trotter showed constructively that the maximum cardinality of a set of mutually non-adjacent edges (matching) is equal to the minimum cardinality of a collection of sets of mutually adjacent edges which cover all edges. The purpose of this note is to give an algorithmic proof that the chromatic index of these graphs is equal to the maximum cardinality of a set of mutually adjacent edges.

Related Organizations

École Polytechnique Fédérale de Lausanne EPFL
Switzerland

Keywords

Graph theory, Coloring of graphs and hypergraphs, Paths and cycles

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