JCT
2008
13 years 10 months ago
2008
Tutte's Wheels-and-Whirls Theorem proves that if M is a 3-connected matroid other than a wheel or a whirl, then M has a
JCT
2008
13 years 10 months ago
2008
Let {a, b, c} be a triangle in a 3-connected matroid M. In this paper, we describe the structure of M relative to {a, b, c} when, for all t in {a, b, c}, either M\t is not 3-connec...
JCT
2007
13 years 11 months ago
2007
A k-triangulation of a convex polygon is a maximal set of diagonals so that no k + 1 of them mutually cross in their interiors. We present a bijection between 2-triangulations of a...
JCT
2007
13 years 11 months ago
2007
We show that for any closed surface F with χ(F) −4 (or χ(F) −2), there exist graphs that triangulate the torus or the Klein bottle (or the projective plane) and that quadran...
JCT
2007
13 years 11 months ago
2007
In answer to a question of Andrews about finding combinatorial proofs of two identities in Ramanujan’s “lost” notebook, we obtain weighted forms of Euler’s theorem on part...
JCT
2006
13 years 11 months ago
2006
A k-majority tournament T on a finite vertex set V is defined by a set of 2k - 1 linear orderings of V, with u v if and only if u lies above v in at least k of the orders. Motiva...
JCT
2006
13 years 11 months ago
2006
Abstract. We introduce "matroid parse trees" which, using only a limited amount of information at each node, can build up the vector representations of matroids of bounde...
JCT
2006
13 years 11 months ago
2006
Kuipers and Veldman conjectured that any 3-connected claw-free graph with order and minimum degree +6 10 is Hamiltonian for sufficiently large. In this paper, we prove that if...
JCT
2006
13 years 11 months ago
2006
JCT
2006
13 years 11 months ago
2006
One of Erdos' favourite conjectures was that any triangle-free graph G on n vertices should contain a set of n/2 vertices that spans at most n2/50 edges. We prove this when t...