A family of multigraphs with large palette index

Maddalena Avesani, Arrigo Bonisoli, Giuseppe Mazzuoccolo

Abstract


Given a proper edge-coloring of a loopless multigraph, the palette of a vertex is defined as the set of colors of the edges which are incident with it. The palette index of a multigraph is defined as the minimum number of distinct palettes occurring among the vertices, taken over all proper edge-colorings of the multigraph itself. In this framework, the palette pseudograph of an edge-colored multigraph is defined in this paper and some of its properties are investigated. We show that these properties can be applied in a natural way in order to produce the first known family of multigraphs whose palette index is expressed in terms of the maximum degree by a quadratic polynomial. We also attempt an analysis of our result in connection with some related questions.

Keywords


Palette index, edge-coloring, interval edge-coloring

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DOI: https://doi.org/10.26493/1855-3974.1528.d41

ISSN: 1855-3974

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