一类平面图中的彩虹匹配
Rainbow Matchings in Planar Graphs
DOI: 10.12677/AAM.2022.111030, PDF, HTML, 下载: 236  浏览: 341 
作者: 余 锐：浙江师范大学数学与计算机科学学院，浙江 金华；王华平：江西师范大学数学与统计学院，江西 南昌
关键词: 匹配；彩虹图；Anti-Ramsey数；Matching； Rainbow Graph； Anti-Ramsey Number
摘要: 对给定的边染色图 G，若图 G 的每条边的颜色都不同，则G是彩虹的。对给定的图 G 和 H，H 在G 上的 anti-Ramsey 数，记作 AR(G, H)，表示图 G 中不包含任何同构千 H 的彩虹子图的最大边染色数。本文主要研究Tn中匹配的 anti-Ramsey 数。
Abstract: We call an edge-colored graph G rainbow, if all of its edges have different colors. The anti-Ramsey number of the graph H in G, denoted by AR(G, H), is the maximum number of colors in an edge-coloring of G which does not contain any rainbow subgraph isomorphic to H. In this paper, we consider the anti-Ramsey number for matchings in planar graphs Tn.
文章引用：余锐, 王华平. 一类平面图中的彩虹匹配[J]. 应用数学进展, 2022, 11(1): 238-245. https://doi.org/10.12677/AAM.2022.111030

参考文献

[1] Erd˝os, P., Simonovits, M. and S´os, V.T. (1973) Anti-Ramsey Theorems. Colloquia Mathematica Societatis J´anos Bolyai, 10, 657-665.
[2] Li, X.L. and Xu, Z.X. (2009) The Rainbow Number of Matchings in Regular Bipartite Graphs. Applied Mathematics Letters, 22, 1525-1528.
https://doi.org/10.1016/j.aml.2009.03.019
[3] Schiermeyer, I. (2004) Rainbow Numbers for Matchings and Complete Graphs. Discrete Math- ematics, 286, 157-162.
[4] Jendrol/, S., Schiermeyer, I. and Tu, J.H. (2014) Rainbow Numbers for Matchings in Plane Triangulations. Discrete Mathematics, 331, 158-164.
https://doi.org/10.1016/j.disc.2014.05.012
[5] Qin, Z.M., Lan, Y.X., Shi, Y.T. and Yue, J. (2021) Exact Rainbow Numbers for Matchings in Plane Triangulations. Discrete Mathematics, 344, Article ID: 112301.
https://doi.org/10.1016/j.disc.2021.112301

为你推荐