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DM
2006
14 years 9 months ago
2006
For a graph G and k a real number, we consider the sum of the k-th powers of the degrees of the vertices of G. We present some general bounds on this sum for various values of k. ...
65
Voted
DM
2006
14 years 9 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...
DM
2006
14 years 9 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...
DM
2006
14 years 9 months ago
2006
We conjecture new sufficient conditions for a digraph to have a Hamilton cycle. In view of applications, the conjecture is of interest in the areas where unitary matrices are of i...
60
Voted
DM
2006
14 years 9 months ago
2006
We answer a question raised by Brass on the number of maximally repeated sub-patterns in a set of n points in Rd. We show that this number, which was conjectured to be polynomial,...