Given a graph G and a positive integer k,define the Gallai–Ramsey number to be the minimum number of vertices n such that any k-edge coloring of Kn contains either a rainbow(all different colored)triangle or a monoch...Given a graph G and a positive integer k,define the Gallai–Ramsey number to be the minimum number of vertices n such that any k-edge coloring of Kn contains either a rainbow(all different colored)triangle or a monochromatic copy of G.In this paper,we obtain exact values of the Gallai–Ramsey numbers for the union of two stars in many cases and bounds in other cases.This work represents the first class of disconnected graphs to be considered as the desired monochromatic subgraph.展开更多
基金Supported by the National Science Foundation of China(Grant Nos.12061059 and 61763041)。
文摘Given a graph G and a positive integer k,define the Gallai–Ramsey number to be the minimum number of vertices n such that any k-edge coloring of Kn contains either a rainbow(all different colored)triangle or a monochromatic copy of G.In this paper,we obtain exact values of the Gallai–Ramsey numbers for the union of two stars in many cases and bounds in other cases.This work represents the first class of disconnected graphs to be considered as the desired monochromatic subgraph.
