On the flip graphs on perfect matchings of complete graphs and signed reversal graphs

TL;DR

This paper explores the combinatorial and spectral properties of flip graphs on perfect matchings of complete graphs, linking them to signed reversal graphs and improving bounds on their chromatic number.

Contribution

It introduces new insights into the structure of flip graphs on perfect matchings and enhances the upper bound on their chromatic number.

Findings

Analyzed the spectral properties of flip graphs.

Connected flip graphs to signed reversal graphs.

Improved the upper bound on chromatic number.

Abstract

In this paper, we study the flip graph on the perfect matchings of a complete graph of even order. We investigate its combinatorial and spectral properties including connections to the signed reversal graph and we improve a previous upper bound on its chromatic number.