树的线图的一般染色数及其在严格距离图上的应用
The Generalized Coloring Number of Line Graph of Trees and Their Application to Exact Distance Graphs

作者: 王嘉琦 :浙江师范大学数学系, 浙江 金华;

关键词: 线图一般染色数着色数严格距离-p 图Line Graph Generalized Coloring Number Chromatic Number Exact Distance-p Graph

摘要:
线图 L(G) 的一般染色数 colk(L(G)) 或者 wcolk(L(G)) 其实就是原图 G  的一般边染色数.  我们将介绍图 G 的一般边染色数来研究线图 L(G) 的一般染色数。对千树 T , 我们用这一关系给出了 colk(L(T )) 和 wcolk(L(T )) 的上界, 并给出了着色数的上界, 其中是线图L(T) 的严格距离-p 图.

Abstract: The generalized coloring number colk(L(G)) or wcolk(L(G)) of a line graph L(G) is just the generalized edge coloring number or of the original graph G. We introduce the generalized edge coloring number of graph G to study the generalized coloring number of the line graph L(G). We use this relation to give the upper bound of colk(L(T )) and wcolk(L(T )) and then give the upper bound of .


Abstract:

文章引用: 王嘉琦 (2021) 树的线图的一般染色数及其在严格距离图上的应用。 应用数学进展, 10, 747-752. doi: 10.12677/AAM.2021.103082

参考文献

[1] Chen, G.T. and Schelp, R.H. (1993) Graphs with Linearly Bounded Ramsey Numbers. Journal of Combinatorial Theory, Series B, 57, 138-149.
https://doi.org/10.1006/jctb.1993.1012

[2] Kierstead, H.A. (2000) A Simple Competitive Graph Coloring Algorithm. Journal of Combi- natorial Theory, Series B, 78, 57-68.
https://doi.org/10.1006/jctb.1999.1927

[3] Kierstead, H.A. and Trotter, W.T. (1994) Planar Graph Coloring with an Uncooperative Partner. Journal of Graph Theory, 18, 569-584.
https://doi.org/10.1002/jgt.3190180605

[4] Kierstead, H.A. and Trotter, W.T. (2001) Competitive Colorings of Oriented Graphs. The Electronic Journal of Combinatorics, 8, Research Paper 12.
https://doi.org/10.37236/1611

[5] Kierstead, H.A. and Yang, D.Q. (2003) Orderings on Graphs and Game Coloring Number. Order, 20, 255-264.
https://doi.org/10.1023/B:ORDE.0000026489.93166.cb

[6] van den Heuvel, J., Kierstead, H.A. and Quiroz, D.A. (2019) Chromatic Numbers of Exact Distance Graphs. Journal of Combinatorial Theory, Series B, 134, 143-163.
https://doi.org/10.1016/j.jctb.2018.05.007

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