一类平面图中的彩虹匹配

Rainbow Matchings in Planar Graphs

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。

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.