A totally (. + 1)-colorable 1-planar graph with girth at least five

Authors
Sun, Lin Wu, Jian Liang Cai, Hua
Citation
Sun, Lin et al., A totally (. + 1)-colorable 1-planar graph with girth at least five, Acta mathematica Sinica. English series (Print) , 32(11), 2016, pp. 1337-1349
Journal title
Acta mathematica Sinica. English series (Print) → ACNP
ISSN journal
14398516
Volume
32
Issue
11
Year of publication
2016
Pages
1337 - 1349
Database
ACNP
SICI code
Abstract
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 prove that every 1-planar graph G with maximum degree .(G) . 12 and girth at least five is totally (.(G) + 1)-colorable.