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Title: The total chromatic number of split-indifference graphs
Authors: Campos, Christiane Neme
Figueiredo, Celina Miraglia Herrera de
Machado, Raphael Carlos Santos
Mello, Celia Picinin de
Keywords: Teoria dos grafos
Teoria da computação
Número cromático
Issue Date: 2012
Citation: CAMPOS, C. N. The total chromatic number of split-indifference graphs. Discrete Mathematics, v. 312, n. 17, p. 2690–2693, 2012.
Abstract: The total chromatic number of a graph G, !T (G), is the least number of colours su!cient to colour the vertices and edges of a graph such that no incident or adjacent elements (vertices or edges) receive the same colour. The Total Colouring Conjecture (TCC) states that every simple graph G has !T (G) ! "(G) + 2 and it is a challenging open problem in Graph Theory. For both split graphs and indifference graphs, the TCC holds and !T (G) = "(G) + 1 when "(G) is even. For a split-indi#erence graph G with odd "(G), we give conditions for its total chromatic number to be "(G) + 2 and we build a ("(G) + 1)-total colouring, otherwise. Also, we pose a conjecture for a class of graphs that generalizes split-indifference graphs
Description: 4 p. : il.
Document type: Artigo / Article
Unit: Divisão de Metrologia em Telecomunicações - Ditel
Appears in Collections:DITER | Artigos publicados em periódicos internacionais

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