Reed conjectured that for every ε > 0 and every integer ∆, there exists g such that the fractional total chromatic number of every graph with maximum degree ∆ and girth at...
The chromatic capacity cap(G) of a graph G is the largest k for which there exists a k-coloring of the edges of G such that, for every coloring of the vertices of G with the same ...
: Jacobson, Levin, and Scheinerman introduced the fractional Ramsey function rf (a1,a2, ...,ak) as an extension of the classical definition for Ramsey numbers. They determined an e...
Let Mad(G) denote the maximum average degree (over all subgraphs) of G and let i(G) denote the injective chromatic number of G. We prove that if Mad(G) 5 2 , then i(G) + 1; sim...
Let mad(G) denote the maximum average degree (over all subgraphs) of G and let i(G) denote the injective chromatic number of G. We prove that if 4 and mad(G) < 14 5 , then i(G...