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Upper bounds for the 2-hued chromatic number of graphs in terms of the independence number

Dehghan, A ; Sharif University of Technology | 2012

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  1. Type of Document: Article
  2. DOI: 10.1016/j.dam.2012.05.003
  3. Publisher: Elsevier , 2012
  4. Abstract:
  5. A 2-hued coloring of a graph G is a coloring such that, for every vertex v∈V(G) of degree at least 2, the neighbors of v receive at least two colors. The smallest integer k such that G has a 2-hued coloring with k colors is called the 2-hued chromatic number of G, and is denoted by χ2(G). In this paper, we will show that, if G is a regular graph, then χ2(G)-χ(G)≤2log 2(α(G))+3, and, if G is a graph and δ(G)<2, then χ2(G)-χ(G)≤1+4 Δ2δ-1⌉(1+log 2Δ(G)2Δ(G)-δ(G)(α(G))), and in the general case, if G is a graph, then χ2(G)-χ(G)≤2+min α′(G),α(G)+ω(G)2
  6. Keywords:
  7. 2-hued chromatic number ; 2-hued coloring ; Independence number ; Probabilistic method ; Chromatic number ; Chromatic number of graphs ; Graph G ; Independence number ; Probabilistic methods ; Regular graphs ; Two-color ; Upper Bound ; Networks (circuits) ; Graph theory
  8. Source: Discrete Applied Mathematics ; Volume 160, Issue 15 , 2012 , Pages 2142-2146 ; 0166218X (ISSN)
  9. URL: http://www.sciencedirect.com/science/article/pii/S0166218X12001977