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Edge-colouring of joins of regular graphs II

Author

Listed:
  • Caterina Simone

    (IASI-CNR)

  • Anna Galluccio

    (IASI-CNR)

Abstract

We prove that the edges of every even graph G=G 1+G 2 that is the join of two regular graphs G 1 and G 2 can be coloured with Δ(G) colours, whenever Δ(G)=Δ(G 1)+|V 2|. The proof of this result together with the results in De Simone and Galluccio (J. Comb. Optim. 18:417–428, 2009) states that every even graph G that is the join of two regular graphs is Class 1. The proof yields an efficient combinatorial algorithm to find a Δ(G)-edge-colouring of this type of graphs.

Suggested Citation

  • Caterina Simone & Anna Galluccio, 2013. "Edge-colouring of joins of regular graphs II," Journal of Combinatorial Optimization, Springer, vol. 25(1), pages 78-90, January.
    • Handle: RePEc:spr:jcomop:v:25:y:2013:i:1:d:10.1007_s10878-011-9420-4
    DOI: 10.1007/s10878-011-9420-4
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    1. Caterina De Simone & Anna Galluccio, 2009. "Edge-colouring of joins of regular graphs, I," Journal of Combinatorial Optimization, Springer, vol. 18(4), pages 417-428, November.
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