EJC
2007
13 years 4 months ago
2007
We present a new family of locally 5–arc transitive graphs. The graphs constructed are bipartite with valency {2m + 1, 2m}. The actions of the automorphism group on the two bipa...
EJC
2007
13 years 4 months ago
2007
We prove a conjecture of F. Chapoton relating certain enumerative invariants of (a) the cluster complex associated by S. Fomin and A. Zelevinsky with a finite root system and (b)...
EJC
2007
13 years 4 months ago
2007
The cone ˆG of a finite graph G is obtained by adding a new vertex p, called the cone point, and joining each vertex of G to p by a simple edge. We show that the rank of the red...
EJC
2007
13 years 4 months ago
2007
Consider a polar space S weakly embedded in a projective space P. A secant of S is the intersection of the point set of S with a line of P spanned by two non-collinear points of S...
EJC
2007
13 years 4 months ago
2007
In [2], we showed the existence of five isomorphism classes of hyperplanes in each dual polar space of type DH(5, q2). We also proved there that every hyperplane of DH(5, q2) bel...
EJC
2007
13 years 4 months ago
2007
We construct algorithms for deciding essentially any minor-closed parameter, with explicit time bounds. This result strengthens previous results by Robertson and Seymour [1,2], Fr...
EJC
2007
13 years 4 months ago
2007
We prove that the translation plane and the shift plane defined by a planar partition function form an oval pair of projective planes in the sense that the planes share a line pe...
EJC
2007
13 years 4 months ago
2007
We develop a theory of representations in Rm for directed strongly regular graphs, which gives a new proof of a nonexistence condition of Jørgensen [8]. We also describe some new...
EJC
2007
13 years 4 months ago
2007
EJC
2007
13 years 4 months ago
2007
It was conjectured by Thomassen ([B. Alspach, C. Godsil, Cycle in graphs, Ann. Discrete Math. 27 (1985)], p. 466) that every longest circuit of a 3-connected graph must have a cho...