The palette of a vertex v of a graph G in a proper edge-coloring is the set of colors assigned to the edges which are incident with v. The palette index of G is the minimum number of palettes occurring among all proper edge-colorings of G. After reviewing some results on the palette index of regular graphs, we consider the problem of determining the palette index for non-regular graphs. We begin by considering the family of trees. We give an upper bound for the palette index of a tree in terms of the maximum degree Δ. We show that this bound is best possible by producing, for each Δ≥ 3, a tree T^ Δ whose palette index reaches the upper bound.

On the palette index of a graph: the case of trees / Bonisoli, Arrigo; Bonvicini, Simona; Mazzuoccolo, Giuseppe. - In: LECTURE NOTES OF SEMINARIO INTERDISCIPLINARE DI MATEMATICA. - ISSN 2284-0206. - 14:(2017), pp. 49-55.

On the palette index of a graph: the case of trees

BONISOLI, Arrigo;BONVICINI, Simona;
2017

Abstract

The palette of a vertex v of a graph G in a proper edge-coloring is the set of colors assigned to the edges which are incident with v. The palette index of G is the minimum number of palettes occurring among all proper edge-colorings of G. After reviewing some results on the palette index of regular graphs, we consider the problem of determining the palette index for non-regular graphs. We begin by considering the family of trees. We give an upper bound for the palette index of a tree in terms of the maximum degree Δ. We show that this bound is best possible by producing, for each Δ≥ 3, a tree T^ Δ whose palette index reaches the upper bound.
14
49
55
On the palette index of a graph: the case of trees / Bonisoli, Arrigo; Bonvicini, Simona; Mazzuoccolo, Giuseppe. - In: LECTURE NOTES OF SEMINARIO INTERDISCIPLINARE DI MATEMATICA. - ISSN 2284-0206. - 14:(2017), pp. 49-55.
Bonisoli, Arrigo; Bonvicini, Simona; Mazzuoccolo, Giuseppe
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11380/1132584
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