Gallai-Ramsey numbers for graphs with five vertices of chromatic number four

Abstract

Given a graph $H$ and an integer $k\ge 1$, the Gallai-Ramsey number $G{R}_k(H)$ is defined to be the minimum integer $n$ such that every $k$-edge coloring of $K_n$ contains either a rainbow (all different colored) triangle or a monochromatic copy of $H$. In this paper, we determine the Gallai-Ramsey numbers for connected graphs with five vertices of chromatic number four.

18 pages, 1 figure. arXiv admin note: text overlap with arXiv:2006.02603

References in corpus (4)

• Ramsey and Gallai-Ramsey numbers for two classes of unicyclic graphs
• Gallai-Ramsey numbers for fans
• Ramsey and Gallai-Ramsey number for wheels
• Gallai-Ramsey numbers for graphs with chromatic number three

Cited by in corpus (1)

• Extremal problems and results related to Gallai-colorings