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» Colouring Random Regular Graphs
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DM
2008
103views more  DM 2008»
13 years 4 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...
WDAG
2000
Springer
112views Algorithms» more  WDAG 2000»
13 years 8 months ago
More Lower Bounds for Weak Sense of Direction: The Case of Regular Graphs
A graph G with n vertices and maximum degree G cannot be given weak sense of direction using less than G colours. It is known that n colours are always sufficient, and it was conje...
Paolo Boldi, Sebastiano Vigna
APPROX
1998
Springer
150views Algorithms» more  APPROX 1998»
13 years 8 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
13 years 11 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
SPAA
2005
ACM
13 years 10 months ago
Peer-to-peer networks based on random transformations of connected regular undirected graphs
We present k-Flipper, a graph transformation algorithm that transforms regular undirected graphs. Given a path of k +2 edges it interchanges the end vertices of the path. By defin...
Peter Mahlmann, Christian Schindelhauer