On edge colorings of 1-toroidal graphs

Authors
Zhang, Xin Liu, Gui Zhen
Citation
Zhang, Xin et Liu, Gui Zhen, On edge colorings of 1-toroidal graphs, Acta mathematica Sinica. English series (Print) , 29(7), 2013, pp. 1421-1428
Journal title
Acta mathematica Sinica. English series (Print) → ACNP
ISSN journal
14398516
Volume
29
Issue
7
Year of publication
2013
Pages
1421 - 1428
Database
ACNP
SICI code
Abstract
A graph is 1-toroidal, if it can be embedded in the torus so that each edge is crossed by at most one other edge. In this paper, it is proved that every 1-toroidal graph with maximum degree . . 10 is of class one in terms of edge coloring. Meanwhile, we show that there exist class two 1-toroidal graphs with maximum degree . for each . .8.