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Journal of the London Mathematical Society 1991 s2-44(2):193-202; doi:10.1112/jlms/s2-44.2.193
© 1991 by London Mathematical Society
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© Oxford University Press

The Total Chromatic Number of Graphs of High Minimum Degree

A. G. Chetwynd, A. J. W. Hilton and Zhao Cheng

Department of Mathematics, University of Lancaster Lancaster LAI 4YF
Department of Mathematics, University of Reading Whiteknights, PO Box 220, Reading RG6 2AX Department of Mathematics, University of West Virginia Morgantown, West Virginia 26506, USA
Department of Mathematics, University of West Virginia Morgantown, West Virginia 26506, USA

If G is a simple graph with minimum degree {delta}(G) satisfying {delta}(G)≥ 5/6 f(|V(G|+1) the total chromatic number conjecture holds; moreover if {delta}(G) ≥ 3/4 |V(G| then {chi}T(G) ≤ {Delta}(G)+3. Also if G has odd order and is regular with d{G) ≥ 1/3{surd}7|(G)| then a necessary and sufficient condition for {chi}T(G) = {Delta}(G)+1 is given.


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