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Adjacent strong edge colorings and total colorings of regular graphs |
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| Authors: | ZhongFu Zhang Douglas R. Woodall Bing Yao JingWen Li XiangEn Chen Liang Bian |
| Affiliation: | (1) Institute of Applied Mathematics, Lanzhou Jiaotong University, Lanzhou, 730070, China;(2) College of Mathematics and Information Science, Northwest Normal University, Lanzhou, 730070, China;(3) School of Mathematical Sciences, University of Nottingham, Nottingham, NG7 2RD, UK;(4) School of Mathematical Sciences, Qufu Normal University, Qufu, 273165, China |
| Abstract: | It is conjectured that X as′(G) = X t (G) for every k-regular graph G with no C 5 component (k ⩾ 2). This conjecture is shown to be true for many classes of graphs, including: graphs of type 1; 2-regular, 3-regular and (|V(G)| - 2)-regular graphs; bipartite graphs; balanced complete multipartite graphs; k-cubes; and joins of two matchings or cycles. This work was supported by National Natural Science Foundation of China (Grant No. 10771091) |
| Keywords: | graph total coloring adjacent strong edge coloring |
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