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Artigo Acesso aberto Revisado por pares
BIBTEX RIS

Total Colourings of Planar Graphs with Large Girth

1998; Elsevier BV; Volume: 19; Issue: 1 Linguagem: Inglês

10.1006/eujc.1997.0152

ISSN

1095-9971

Autores

O. V. Borodin, Alexandr Kostochka, Douglas R. Woodall,

Tópico(s)

Graph Labeling and Dimension Problems

Resumo

It is proved that ifGis a planar graph with total (vertex–edge) chromatic number χ″, maximum degree Δ and girthg, then χ″ = Δ+1 if Δ ≥ 5 andg ≥ 5, or Δ ≥ 4 andg ≥ 6, or Δ ≥ 3 andg ≥ 10. These results hold also for graphs in the projective plane, torus and Klein bottle.

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