Journal of Graph Theory · 1992 · 13 citations · 6 references
Natural SciencesMathematicsColor TheoryCombinatoricsNumber TheoryCombinatorial Number TheoryEnumerative CombinatoricsGraph ColoringGraph TheoryChromatic PolynomialsTotal Coloring
Abstract Rosenfeld (1971) proved that the Total Colouring Conjecture holds for balanced complete r ‐partite graphs. Bermond (1974) determined the exact total chromatic number of every balanced complete r ‐partite graph. Rosenfeld's result had been generalized recently to complete r ‐partite graphs by Yap (1989). The main result of this paper is to prove that the total chromatic number of every complete r ‐partite graph G of odd order is Δ ( G ) + 1. This result gives a partial generalization of Bermond's theorem.
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SOME UNSOLVED PROBLEMS IN GRAPH THEORY
V. G. Vizing · Russian Mathematical Surveys · 1968 · 436 citations
On the total coloring of certain graphs
Moshe Rosenfeld · Israel Journal of Mathematics · 1971 · 142 citations
Hian-Poh Yap · Bulletin of the London Mathematical Society · 1989 · 96 citations