Coloring and the Lonely Graph

Abstract

We improve upper bounds on the chromatic number proven independently in [1] and [5]. Our main lemma gives a sufficient condition for two paths in graph to be completely joined. Using this, we prove that if a graph has an optimal coloring with more than ω2 singleton color classes, then it satisfies χ ≤ ω+∆+1 2 . It follows that a graph satisfying n… (More)

Topics

  • Presentations referencing similar topics