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» Frugal Colouring of Graphs
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DM
2008
95views more  DM 2008»
14 years 10 months ago
General neighbour-distinguishing index of a graph
It is proved that edges of a graph G with no component K2 can be coloured using at most 2 log2 (G) + 1 colours so that any two adjacent vertices have distinct sets of colours of t...
Ervin Györi, Mirko Hornák, Cory Palmer...
SIROCCO
2000
14 years 11 months ago
Lower bounds for (weak) sense of direction
A graph with n vertices and maximum degree cannot be given weak sense of direction using less than colours. It is known that n colours are always sufficient, but it has been conje...
Paolo Boldi, Sebastiano Vigna
DAM
2011
14 years 4 months ago
Powers of cycles, powers of paths, and distance graphs
In 1988, Golumbic and Hammer characterized powers of cycles, relating them to circular-arc graphs. We extend their results and propose several further structural characterizations ...
Min Chih Lin, Dieter Rautenbach, Francisco J. Soul...
DM
2008
103views more  DM 2008»
14 years 10 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»
15 years 2 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