On Validity of Reed Conjecture for {P_5, Flag^C}-free graphs

TL;DR

This paper proves Reed's conjecture for a specific class of graphs that exclude certain subgraphs, extending known results and contributing to the understanding of graph coloring conjectures.

Contribution

It establishes the validity of Reed's conjecture for {P5, Flag^C}-free graphs, a previously unresolved case, and derives known results as corollaries.

Findings

Reed's conjecture holds for {P5, Flag^C}-free graphs.

Some known results are recovered as corollaries.

The conjecture remains open in the general case.

Abstract

Here we prove that Reed Conjecture is valid for {P5, Flag_Complement}-free graphs where FlagComplement is the complement of the Flag graph. Some of the known results follow as corollaries to our result. Reed conjecture is still open in general.