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Edge-choosability in line-perfect multigraphs. (English) Zbl 0928.05017
Discrete Math. 202, No. 1-3, 191-199 (1999); erratum ibid. 260, No. 1-3, 323-326 (2003).
A multigraph is said to be line-perfect if its line graph is perfect. In this paper it is proved that if every edge \(e\) of a line-perfect multigraph \(G\) is given a list containing at least as many colors as there are edges in a largest edge-clique containing \(e\), then \(G\) can be edge-colored from its list. This leads to several characterizations of line-perfect multigraphs in terms of edge-choosability properties. It also proves that these multigraphs satisfy the list-coloring conjecture, which states that if every edge of \(G\) is given a list of \(\chi '(G)\) colors (where \(\chi ' \) denotes the chromatic index) then \(G\) can be edge-colored from its lists. Since bipartite multigraphs are line-perfect, this generalizes F. Galvin’s result [J. Comb. Theory, Ser. B 63, No. 1, 153-158 (1995; Zbl 0826.05026)] that the conjecture holds for bipartite multigraphs.

MSC:
05C15 Coloring of graphs and hypergraphs
05C17 Perfect graphs
05C75 Structural characterization of families of graphs
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References:
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