Highly Influential

4 Excerpts

- Published 2016 in Graphs and Combinatorics

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).

@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}
}