Plane graphs with maximum degree 7 and without 5-cycles with chords are 8-totally-colorable

2011 ◽  
Vol 41 (1) ◽  
pp. 95-104 ◽  
Author(s):  
Qiang SUN ◽  
Xin SHEN Lan TAO ◽  
岚 沈 ◽  
YingQian WANG
Keyword(s):  
Maximum Degree ◽  
Plane Graphs

Plane graphs of maximum degree Δ ≥ 7 are edge‐face (Δ + 1)‐colorable

2020 ◽  
Vol 95 (1) ◽  
pp. 99-124
Author(s):  
Yiqiao Wang ◽  
Xiaoxue Hu ◽  
Weifan Wang ◽  
Ko‐Wei Lih
Keyword(s):  
Maximum Degree ◽  
Plane Graphs

EDGE-FACE CHROMATIC NUMBER OF 2-CONNECTED PLANE GRAPHS WITH HIGH MAXIMUM DEGREE

2006 ◽  
Vol 26 (3) ◽  
pp. 477-482
Author(s):  
Zhongfu Zhang ◽  
Weifan Wang ◽  
Jingwen Li ◽  
Bing Yao ◽  
Yuehua Bu
Keyword(s):  
Chromatic Number ◽  
Maximum Degree ◽  
Plane Graphs ◽  
High Maximum

Plane Graphs with Maximum Degree Δ≥8 Are Entirely (Δ+3)-Colorable

2012 ◽  
Vol 73 (3) ◽  
pp. 305-317 ◽  
Author(s):  
Yingqian Wang ◽  
Xianghua Mao ◽  
Zhengke Miao
Keyword(s):  
Maximum Degree ◽  
Plane Graphs

scholarly journals Plane graphs with maximum degree 9 are entirely 11-choosable

2016 ◽  
Vol 339 (11) ◽  
pp. 2742-2753
Author(s):  
Xiaoxue Hu ◽  
Weifan Wang ◽  
Wai Chee Shiu ◽  
Yiqiao Wang
Keyword(s):  
Maximum Degree ◽  
Plane Graphs

scholarly journals Total-Coloring of Plane Graphs with Maximum Degree Nine

2008 ◽  
Vol 22 (4) ◽  
pp. 1462-1479 ◽  
Author(s):  
Łukasz Kowalik ◽  
Jean-Sébastien Sereni ◽  
Riste Škrekovski
Keyword(s):  
Maximum Degree ◽  
Total Coloring ◽  
Plane Graphs

scholarly journals Edge-face coloring of plane graphs with maximum degree nine

2010 ◽  
Vol 66 (4) ◽  
pp. 332-346 ◽  
Author(s):  
Jean-Sébastien Sereni ◽  
Matěj Stehlík
Keyword(s):  
Maximum Degree ◽  
Plane Graphs

Plane Graphs with Maximum Degree 6 are Edge-face 8-colorable

2013 ◽  
Vol 30 (4) ◽  
pp. 861-874 ◽  
Author(s):  
Min Chen ◽  
André Raspaud ◽  
Weifan Wang
Keyword(s):  
Maximum Degree ◽  
Plane Graphs

scholarly journals Even Subgraph Expansions for the Flow Polynomial of Planar Graphs with Maximum Degree at Most 4

10.37236/7411 ◽  
2018 ◽  
Vol 25 (2) ◽  
Author(s):  
Qingying Deng ◽  
Xian'an Jin ◽  
Fengming Dong ◽  
Eng Guan Tay
Keyword(s):  
Planar Graphs ◽  
Maximum Degree ◽  
Knot Theory ◽  
Close Relation ◽  
Plane Graphs ◽  
Special Cases ◽  
Flow Polynomial ◽  
Kauffman Polynomial

As projections of links, 4-regular plane graphs are important in combinatorial knot theory. The flow polynomial of 4-regular plane graphs has a close relation with the two-variable Kauffman polynomial of links. F. Jaeger in 1991 provided even subgraph expansions for the flow polynomial of cubic plane graphs. Starting from and based on Jaeger's work, by introducing splitting systems of even subgraphs, we extend Jaeger's results from cubic plane graphs to plane graphs with maximum degree at most 4 including 4-regular plane graphs as special cases. Several consequences are derived and further work is discussed.

scholarly journals On (p,1)-total labelling of plane graphs with independent crossings

Filomat ◽  
2012 ◽  
Vol 26 (6) ◽  
pp. 1091-1100 ◽  
Author(s):  
Xin Zhang ◽  
Guizhen Liu ◽  
Yong Yu
Keyword(s):  
Planar Graph ◽  
Planar Graphs ◽  
Maximum Degree ◽  
Discrete Math ◽  
Plane Graph ◽  
Plane Graphs ◽  
High Maximum ◽  
Crossed Pair ◽  
Large Girth

Two distinct crossings are independent if the end-vertices of the crossed pair of edges are mutually different. If a graph G has a drawing in the plane so that every two crossings are independent, then we call G a plane graph with independent crossings or IC-planar graph for short. In this paper, it is proved that the (p, 1)-total labelling number of every IC-planar graph G is at most ?(G) + 2p ? 2 provided that ?(G) ? ? and 1(G) ? 1, where (?, 1) ? {(6p + 2, 3), (4p + 2, 4), (2p + 5, 5)}. As a consequence, we generalize and improve some results obtained in [F. Bazzaro, M. Montassier, A. Raspaud, (d, 1)-Total labelling of planar graphs with large girth and high maximum degree, Discrete Math. 307 (2007) 2141-2151].

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