Anti-Ramsey numbers for three classes of special subgraphs in wheel graph(轮图中三类特殊子图的anti-Ramsey数)

Abstract

A subgraph in an edge-colored graph is called rainbow, if all its edges have different colors. Given two graphs G and H, the anti-Ramsey number for H in G, denoted by ar(G,H), is the maximum number of colors in an edge-coloring of G such that G contains no rainbow copy of H. In this paper, we determine the exact values of the anti-Ramsey numbers for Theta, star, double star graph when the host graph G is wheel graph.(在边染色图中，如果某个子图的每条边都染不同的颜色,则称该子图是彩虹的。给定图G和H，对图G的一个k边染色若存在最大的正整数R，使得G中不包含彩虹的H作为子图，则将H的anti-Ramsey数记为ar(G,H)。当主图为轮图时，给出了Theta图、星图和双星图anti-Ramsey数的精确值。)

Keywords

• wheel graph(轮图)
• anti-ramsey number(anti-ramsey数)
• theta graph(theta图)
• star graph(星图)
• double star graph(双星图)