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.
AMS subject classification codes (1991)05 C 15 05 C 70 90 C 10
Unable to display preview. Download preview PDF.
- M. Behzad: Graphs and their chromatic numbers,Doctoral Thesis (Michigan State University)., (1965).Google Scholar
- J. Edmonds: Maximum matching and a polyhedron with 0,1 vertices,Journal of Research of the National Bureau of Standards (B) 69 (1965), 125–130.Google Scholar
- D. R. Fulkerson: Anti-blocking polyhedra,J. Combinatorial Theory B 12 (1972). 50–71.Google Scholar
- H. R. Hind: An upper bound on the total chromatic number.,Graphs and Combinatorics 6 (1990), 153–158.Google Scholar
- J. Ryan: Fractional total colouring,Discrete Appl. Math. 27 (1990), 287–292.Google Scholar
- N. Vijayaditya: On the total chromatic number of a graph,J. London Math. Soc. (2)3 (1971), 405–408.Google Scholar
- V. G. Vizing: Some unsolved problems in graph theory (in Russian),Uspekhi Math. Nauk. 23 (1968), 117–134.Google Scholar