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» Chromatic Ramsey numbers
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IPL
2008
145views more  IPL 2008»
13 years 7 months ago
Complexity analysis of a decentralised graph colouring algorithm
Colouring a graph with its chromatic number of colours is known to be NP-hard. Identifying an algorithm in which descisions are made locally with no information about the graph�...
Ken R. Duffy, N. O'Connell, Artëm Sapozhnikov
ENDM
2007
68views more  ENDM 2007»
13 years 7 months ago
List Colouring Squares of Planar Graphs
In 1977, Wegner conjectured that the chromatic number of the square of every planar graph G with maximum degree ∆ ≥ 8 is at most 3
Frédéric Havet, Jan van den Heuvel, ...
JCT
2010
70views more  JCT 2010»
13 years 5 months ago
Graphs with bounded tree-width and large odd-girth are almost bipartite
We prove that for every k and every ε > 0, there exists g such that every graph with tree-width at most k and odd-girth at least g has circular chromatic number at most 2 + ε...
Alexandr V. Kostochka, Daniel Král', Jean-S...
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...
JCT
2008
86views more  JCT 2008»
13 years 7 months ago
On distinguishing trees by their chromatic symmetric functions
Let T be an unrooted tree. The chromatic symmetric function XT , introduced by Stanley, is a sum of monomial symmetric functions corresponding to proper colorings of T . The subtre...
Jeremy L. Martin, Matthew Morin, Jennifer D. Wagne...