A note on total colorings of planar graphs without 4-cycles

• Autorzy: Ping Wang , Jian-Liang Wu
• Języki publikacji: EN

Abstrakty

EN

Let G be a 2-connected planar graph with maximum degree Δ such that G has no cycle of length from 4 to k, where k ≥ 4. Then the total chromatic number of G is Δ +1 if (Δ,k) ∈ {(7,4),(6,5),(5,7),(4,14)}.

Słowa kluczowe

EN

total coloring; planar graph; list coloring; girth

Kategorie tematyczne

• 05C15: Coloring of graphs and hypergraphs

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2004
• Tom: 24
• Numer: 1
• Strony: 125-135

Daty

wydano

2004

otrzymano

2002-02-26

poprawiono

2003-10-21

Twórcy

autor

Ping Wang

• Department of Mathematics, Statistics and Computer Science, St. Francis Xavier University, Antigonish, Nova Scotia, Canada

autor

Jian-Liang Wu

• School of Mathematics, Shandong University, Jinan, Shandong, 250100, P.R. China

Bibliografia

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• [3] O.V. Borodin, A.V. Kostochka and D.R. Woodall, Total colorings of planar graphs with large maximum degree, J. Graph Theory 26 (1997) 53-59, doi: 10.1002/(SICI)1097-0118(199709)26:1<53::AID-JGT6>3.0.CO;2-G
• [4] O.V. Borodin, A.V. Kostochka and D.R. Woodall, Total colourings of planar graphs with large girth, European J. Combin. 19 (1998) 19-24, doi: 10.1006/eujc.1997.0152.
• [5] O.V. Borodin, A.V. Kostochka and D.R. Woodall, List edge and list total colourings of multigarphs, J. Combin. Theory (B) 71 (1997) 184-204, doi: 10.1006/jctb.1997.1780.
• [6] J.L. Gross and T.W. Tucker (Topological Graph Theory, John and Wiley & Sons, 1987).
• [7] A.J.W. Hilton, Recent results on the total chromatic number, Discrete Math. 111 (1993) 323-331, doi: 10.1016/0012-365X(93)90167-R.
• [8] T.R. Jensen and B. Toft (Graph Coloring Problems, John Wiley & Sons, 1995).
• [9] Peter C.B. Lam, B.G. Xu, and J.Z. Liu, The 4-choosability of plane graphs without 4-cycles, J. Combin. Theory (B) 76 (1999) 117-126, doi: 10.1006/jctb.1998.1893.
• [10] A. Sanchez-Arroyo, Determining the total coloring number is NP-hard, Discrete Math. 78 (1989) 315-319, doi: 10.1016/0012-365X(89)90187-8.
• [11] H.P. Yap, Total colourings of graphs, Lecture Notes in Mathematics 1623 (Springer, 1996).

Identyfikatory

DOI

10.7151/dmgt.1219