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» On the adaptable chromatic number of graphs
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SIAMDM
2010
138views more  SIAMDM 2010»
13 years 5 months ago
The Last Fraction of a Fractional Conjecture
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...
Frantisek Kardos, Daniel Král', Jean-S&eacu...
DM
2008
106views more  DM 2008»
13 years 7 months ago
Chromatic capacity and graph operations
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 ...
Jack Huizenga
JGT
2010
103views more  JGT 2010»
13 years 5 months ago
Proof of a conjecture on fractional Ramsey numbers
: 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...
Jason Brown, Richard Hoshino
DM
2010
78views more  DM 2010»
13 years 7 months ago
Injective colorings of sparse graphs
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...
Daniel W. Cranston, Seog-Jin Kim, Gexin Yu
CORR
2010
Springer
93views Education» more  CORR 2010»
13 years 7 months ago
Injective colorings of graphs with low average degree
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...
Daniel W. Cranston, Seog-Jin Kim, Gexin Yu