论文信息 - Total chromatic number of graphs of odd order and high degree

Total chromatic number of graphs of odd order and high degree

Abstract The total chromatic number χ T ( G ) of a graph G is the least number of colours needed to colour the edges and vertices of G so that no incident or adjacent elements receive the same colour. This paper shows that if G has odd order, minimum degree δ ( G ) and r ( G ) vertices of maximum degree Δ ( G ) such that δ(G)+Δ(G)⩾ 3 2 |V(G)|+r(G)+ 5 2 , then χ T ( G )= Δ ( G )+1.

K. H. Chew

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