Multicolor star-critical Ramsey numbers and Ramsey-good graphs

Abstract

This paper seeks to develop the multicolor version of star-critical Ramsey numbers, which serve as a measure of the strength of the corresponding Ramsey numbers. We offer several general theorems, some of which focus on Ramsey-good cases (i.e., cases in which the corresponding Ramsey number is equal to a general lower bound). We also prove some specific cases for small graphs, and conclude with a table of known multicolor star-critical Ramsey numbers.

Keywords

• deleted edge number, ramsey minimal, size ramsey number