﻿ 树的线图的一般染色数及其在严格距离图上的应用

# 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

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:

[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

Top