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105
Voted
DM
2006
15 years 1 months ago
2006
It is easy to deduce from Ramsey's Theorem that, given positive integers a1, a2, . . . , am and a finite colouring of the set N of positive integers, there exists an injectiv...
98
Voted
DM
2006
15 years 1 months ago
2006
We study the problem of minimal triangulation of graphs. One of the first algorithms to solve this problem was Lex M, which was presented in 1976. A new algorithm, and a simplific...
88
Voted
DM
2006
15 years 1 months ago
2006
For an integer n 3, a rank-n matroid is called an n-spike if it consists of n three-point lines through a common point such that, for all k {1, 2, . . . , n - 1}, the union of e...
DM
2006
15 years 1 months ago
2006
We give an algorithmic characterisation of finite cop-win digraphs. The case of k > 1 cops and k l 1 robbers is then reduced to the one cop case. Similar characterisations are ...
87
Voted
DM
2006
15 years 1 months ago
2006
A graph is called biclaw-free if it has no biclaw as an induced subgraph. In this note, we prove that if G is a connected bipartite biclaw-free graph with (G) 5, then G is collap...