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.
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References
L. Lovasz, “Normal hypergraphs and the perfect graph conjecture”,Discrete Mathematics 2 (1972) 253–267.
L.E. Trotter, Jr., “Line perfect graphs”,Mathematical Programming 12 (1977) 255–259.
D. de Werra, “On good and equitable edge colorings”,Cahiers du Centre d'Etudes de Recherche Opérationelle 17 (2–3–4) (1975) 417–426. [Errata in Cahiers du C.E.R.O. 18 (1–2) (1976) 255.]
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de Werra, D. On line perfect graphs. Mathematical Programming 15, 236–238 (1978). https://doi.org/10.1007/BF01609025
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DOI: https://doi.org/10.1007/BF01609025