An exact value for the Ramsey number $R(K_5, K_{5-e})$

TL;DR

This paper determines the exact value of the Ramsey number R(K_5, K_{5-e}), establishing it as 30, which contributes to the precise understanding of these classical combinatorial parameters.

Contribution

The paper provides the first exact value for R(K_5, K_{5-e}), advancing the knowledge of specific Ramsey numbers involving complete and nearly complete graphs.

Findings

R(K_5, K_{5-e}) = 30

Confirmed the value through computational and combinatorial methods

Contributes to the database of known Ramsey numbers

Abstract

We compute the exact value of the Ramsey number $R(K_5, K_{5-e})$. It is equal to 30.