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COMBINATORICS
2006
14 years 9 months ago
2006
It is proved that, if G is a K4-minor-free graph with maximum degree 3, then G is totally 4-choosable; that is, if every element (vertex or edge) of G is assigned a list of 4 colo...
COMBINATORICS
2006
14 years 9 months ago
2006
In the game G0 two players alternate removing positive numbers of counters from a single pile and the winner is the player who removes the last counter. On the first move of the g...
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COMBINATORICS
2006
14 years 9 months ago
2006
For undirected graphs it has been known for some time that one can bound the diameter using the eigenvalues. In this note we give a similar result for the diameter of strongly con...
COMBINATORICS
2006
14 years 9 months ago
2006
A proper edge colouring of a graph is neighbour-distinguishing if for all pairs of adjacent vertices v, w the set of colours appearing on the edges incident with v is not equal to...
COMBINATORICS
2006
14 years 9 months ago
2006
We give a new derivation of the threshold of appearance of the k-core of a random graph. Our method uses a hybrid model obtained from a simple model of random graphs based on rand...