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Some criteria for a graph to be Class 1

Akbari, S ; Sharif University of Technology | 2012

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  1. Type of Document: Article
  2. DOI: 10.1016/j.disc.2011.09.035
  3. Publisher: Elsevier , 2012
  4. Abstract:
  5. Let G be a graph. The core of G, denoted by GΔ, is the subgraph of G induced by the vertices of degree Δ(G), where Δ(G) is the maximum degree of G. A k-edge coloring of a graph G is a function f:E(G)L, where |L|=k and f( e1)≠f( e2), for every two adjacent edges e1, e2 of G. The edge chromatic number of G, denoted by χ′(G), is the minimum number k for which G has a k-edge coloring. A graph G is said to be Class 1 if χ′(G)= Δ(G) and Class 2 if χ′(G)=Δ(G)+1. In this paper, it is shown that, for every connected graph of even order, if GΔ= C6, then G is Class 1. Also, we prove that, if G is a connected graph, and every connected component of GΔ is a unicyclic graph or a tree, and GΔ is not a disjoint union of cycles, then G is Class 1
  6. Keywords:
  7. Class 1 ; Core ; Edge coloring ; Unicyclic
  8. Source: Discrete Mathematics ; Volume 312, Issue 17 , September , 2012 , Pages 2593-2598 ; 0012365X (ISSN)
  9. URL: http://www.sciencedirect.com/science/article/pii/S0012365X11004493