On Edge Colorings of 1-Toroidal Graphs  

作　　者：Xin ZHANG Gui Zhen LIU 

机构地区：[1]Department of Mathematics, Xidian University [2]School of Mathematics, Shandong University

出　　处：《Acta Mathematica Sinica,English Series》2013年第7期1421-1428,共8页数学学报（英文版）

基　　金：supported by National Natural Science Foundation of China (Grant No. 11026184);supported by National Natural Science Foundation of China (Grant No. 61070230);Research Fund for the Doctoral Program of Higher Education (Grant No. 20100131120017);the Fundamental Research Funds for the Central Universities

摘　　要：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 A ≤ 8.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 A ≤ 8.

关 键 词：1-Toroidal graph 1-planar graph edge coloring 

分 类 号：O157.5[理学—数学]