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JCT

2008

12 years 12 days 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

12 years 12 days 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

12 years 1 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

12 years 1 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

12 years 1 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

12 years 1 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

12 years 1 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

12 years 1 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

12 years 1 months ago
2006

JCT

2006

12 years 1 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...