Fractionally colouring total graphs

Abstract

Bchzad and Vizing have conjectured that given any simple graph of maximum degree Δ, one can colour its edges and vertices with Δ+2 colours so that no two adjacent vertices, or two incident edges, or an edge and either of its ends receive the same colour. We show that for any simple graphG, V(G)ϒE(G) can be fractionally coloured with Δ+2 colours.

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Kilakos, K., Reed, B. Fractionally colouring total graphs. Combinatorica 13, 435–440 (1993). https://doi.org/10.1007/BF01303515

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AMS subject classification codes (1991)

  • 05 C 15
  • 05 C 70
  • 90 C 10