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

Discussiones Mathematicae Graph Theory (2004)

- Volume: 24, Issue: 1, page 125-135
- ISSN: 2083-5892

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topPing Wang, and Jian-Liang Wu. "A note on total colorings of planar graphs without 4-cycles." Discussiones Mathematicae Graph Theory 24.1 (2004): 125-135. <http://eudml.org/doc/270290>.

@article{PingWang2004,

abstract = {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)\}.},

author = {Ping Wang, Jian-Liang Wu},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {total coloring; planar graph; list coloring; girth; chromatic number},

language = {eng},

number = {1},

pages = {125-135},

title = {A note on total colorings of planar graphs without 4-cycles},

url = {http://eudml.org/doc/270290},

volume = {24},

year = {2004},

}

TY - JOUR

AU - Ping Wang

AU - Jian-Liang Wu

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

JO - Discussiones Mathematicae Graph Theory

PY - 2004

VL - 24

IS - 1

SP - 125

EP - 135

AB - 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)}.

LA - eng

KW - total coloring; planar graph; list coloring; girth; chromatic number

UR - http://eudml.org/doc/270290

ER -

## References

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- [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. Zbl0931.05036
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- [11] H.P. Yap, Total colourings of graphs, Lecture Notes in Mathematics 1623 (Springer, 1996). Zbl0839.05001

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