Coloring and the Lonely Graph


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)


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