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The Chromatic Index of a Graph Whose Core is a Cycle of Order at Most 13

Akbari, S ; Sharif University of Technology

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  1. Type of Document: Article
  2. DOI: 10.1007/s00373-013-1317-9
  3. Abstract:
  4. 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) denotes the maximum degree of G. A k -edge coloring of G is a function f: E(G) → L such that {pipe}L{pipe} = k and f(e1) ≠ f(e2) for all two adjacent edges e1 and e2 of G. The chromatic index 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 every connected graph G of even order whose core is a cycle of order at most 13 is Class 1
  5. Keywords:
  6. Class 1 ; Core ; Edge coloring
  7. Source: Graphs and Combinatorics ; Vol. 30, issue. 4 , 2014 , p. 801-819
  8. URL: http://link.springer.com/article/10.1007%2Fs00373-013-1317-9