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JCT
2011
13 years 2 months ago
2011
We consider the problem of orienting the edges of the n-dimensional hypercube so only two different in-degrees a and b occur. We show that this can be done, for two specified in...
JCT
2010
13 years 2 months ago
2010
Let Sm be the set of symmetric bilinear forms on an m-dimensional vector space over GF(q), where q is a power of two. A subset Y of Sm is called an (m, d)-set if the difference of...
JCT
2010
13 years 6 months ago
2010
A graph G on n vertices is Hamiltonian if it contains a cycle of length n and pancyclic if it contains cycles of length for all 3 ≤ ≤ n. Write α(G) for the independence numbe...
JCT
2010
13 years 6 months ago
2010
In the symmetric group on a set of size 2n, let P2n denote the conjugacy class of involutions with no fixed points (equivalently, we refer to these as “pairings”, since each ...
JCT
2010
13 years 6 months ago
2010
The vertex Folkman number F(r, n, m), n < m, is the smallest integer t such that there exists a Km-free graph of order t with the property that every r-coloring of its vertices...