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» Colouring Random 4-Regular Graphs
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DM
2008
116views more  DM 2008»
13 years 7 months ago
Total and fractional total colourings of circulant graphs
In this paper, the total chromatic number and fractional total chromatic number of circulant graphs are studied. For cubic circulant graphs we give upper bounds on the fractional ...
Riadh Khennoufa, Olivier Togni
DM
2008
103views more  DM 2008»
13 years 7 months ago
Improper colouring of (random) unit disk graphs
For any graph G, the k-improper chromatic number k (G) is the smallest number of colours used in a colouring of G such that each colour class induces a subgraph of maximum degree ...
Ross J. Kang, Tobias Müller, Jean-Séba...
APPROX
1998
Springer
150views Algorithms» more  APPROX 1998»
13 years 12 months ago
Approximating Circular Arc Colouring and Bandwidth Allocation in All-Optical Ring Networks
We present randomized approximation algorithms for the circular arc graph colouring problem and for the problem of bandwidth allocation in all-optical ring networks. We obtain a fa...
Vijay Kumar
FCT
2009
Springer
14 years 2 months ago
Martingales on Trees and the Empire Chromatic Number of Random Trees
We study the empire colouring problem (as defined by Percy Heawood in 1890) for maps whose dual planar graph is a tree, with empires formed by exactly r countries. We prove that, ...
Colin Cooper, Andrew R. A. McGrae, Michele Zito
DMTCS
2006
66views Mathematics» more  DMTCS 2006»
13 years 7 months ago
On randomly colouring locally sparse graphs
We consider the problem of generating a random q-colouring of a graph G = (V, E). We consider the simple Glauber Dynamics chain. We show that if for all v V the average degree of...
Alan M. Frieze, Juan Vera