On Total Colorings of Some Special 1-planar Graphs

被引：0

作者：

Lin SUN ^{[1
,2
]}

Jian-liang WU ^{[1
]}

Hua CAI ^{[1
,2
]}

机构：

[1] Department of Mathematics, Changji University

[2] School of Mathematics, Shandong University

来源：

Acta Mathematicae Applicatae Sinica | 2017年 / 33卷 / 03期

关键词：

1-planar graph; total coloring; discharging method; girth; r-minimal graph;

D O I：

暂无

中图分类号：

O157.5 [图论];

学科分类号：

070104 ;

摘要：

A graph is 1-planar if it can be drawn on the plane so that each edge is crossed by at most one other edge. In this paper, we verify the total coloring conjecture for every 1-planar graph G if either ?(G) ≥ 9 and g(G) ≥ 4, or ?(G) ≥ 7 and g(G) ≥ 5, where ?(G) is the maximum degree of G and g(G) is the girth of G.

引用

页码：607 / 618

页数：12

共 50 条

[41] The Vertex Arboricity of 1-Planar Graphs
Zhang, Dongdong
Liu, Juan
Li, Yongjie
Yang, Hehua
GRAPHS AND COMBINATORICS, 2024, 40 (05)
[42] Counting cliques in 1-planar graphs
Gollin, J. Pascal
Hendrey, Kevin
Methuku, Abhishek
Tompkins, Casey
Zhang, Xin
EUROPEAN JOURNAL OF COMBINATORICS, 2023, 109
[43] LINEAR ARBORICITY OF 1-PLANAR GRAPHS
Wang, Weifan
Liu, Juan
Wang, Yiqiao
DISCUSSIONES MATHEMATICAE GRAPH THEORY, 2024, 44 (02) : 435 - 457
[44] Remarks on the joins of 1-planar graphs
Ouyang, Zhangdong
Ge, Jun
Chen, Yichao
APPLIED MATHEMATICS AND COMPUTATION, 2019, 362
[45] The Stub Resolution of 1-Planar Graphs
Kaufmann, Michael
Kratochvil, Jan
Lipp, Fabian
Montecchiani, Fabrizio
Raftopoulou, Chrysanthi
Valtr, Pavel
WALCOM: ALGORITHMS AND COMPUTATION (WALCOM 2020), 2020, 12049 : 170 - 182
[46] Packing trees into 1-planar graphs
De Luca F.
Di Giacomo E.
Hong S.-H.
Kobourov S.
Lenhart W.
Liotta G.
Meijer H.
Tappini A.
Wismath S.
Journal of Graph Algorithms and Applications, 2021, 25 (02) : 605 - 624
[47] Packing Trees into 1-Planar Graphs
De Luca, Felice
Di Giacomo, Emilio
Hong, Seok-Hee
Kobourov, Stephen
Lenhart, William
Liotta, Giuseppe
Meijer, Henk
Tappini, Alessandra
Wismath, Stephen
WALCOM: ALGORITHMS AND COMPUTATION (WALCOM 2020), 2020, 12049 : 81 - 93
[48] On RAC drawings of 1-planar graphs
Bekos, Michael A.
Didimo, Walter
Liotta, Giuseppe
Mehrabi, Saeed
Montecchiani, Fabrizio
THEORETICAL COMPUTER SCIENCE, 2017, 689 : 48 - 57
[49] On drawings and decompositions of 1-planar graphs
Czap, Julius
Hudak, David
ELECTRONIC JOURNAL OF COMBINATORICS, 2013, 20 (02):
[50] The stub resolution of 1-planar graphs
Kaufmann, Michael
Kratochvíl, Jan
Lipp, Fabian
Montecchiani, Fabrizio
Raftopoulou, Chrysanthi
Valtr, Pavel
Journal of Graph Algorithms and Applications, 2021, 25 (02) : 625 - 642

← 1 2 3 4 5 →