Max-Coloring of Vertex-Weighted Graphs

Abstract

A proper vertex coloring of a graph G is a partition {A1, A2, . . . , Ak} of the vertex set V (G) into stable sets. For a graph G with a positive vertexweight c : V (G) → (0,∞), denoted by (G, c), let χ(G, c) be the minimum value of ∑k i=1 maxv∈Ai c(v) over all proper vertex coloring {A1, A2, . . . , Ak} of G and χ(G, c) the minimum value of k for a proper vertex coloring {A1, A2, . . . , Ak} of G such that ∑k i=1 maxv∈Ai c(v) = χ(G, c). This paper establishes an upper bound on χ(G, c) for a weighted r -colorable graph (G, c), and a Nordhaus–Gaddum type inequality for χ(G, c). It also studies the c-perfection for a weighted graph (G, c).

DOI: 10.1007/s00373-015-1562-1

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Cite this paper

@article{Hsu2016MaxColoringOV, title={Max-Coloring of Vertex-Weighted Graphs}, author={Hsiang-Chun Hsu and Gerard J. Chang}, journal={Graphs and Combinatorics}, year={2016}, volume={32}, pages={191-198} }