Domenico Labbate

2-factor Hamiltonian graphs

The Heawood graph and K3, 3 have the property that all of their 2-factors are Hamilton circuits. We call such graphs 2-factor hamiltonian. We prove that if G is a k-regular bipartite 2- factor hamiltonian graph then either G is a circuit or k = 3. Furthermore, we construct an infinite family of cubic bipartite 2-factor hamiltonian graphs based on the Heawood graph and K3,3 and conjecture that these are the only such graphs.

Families of small regular graphs of girth 5

In this paper we are interested in the {\it{Cage Problem}} that consists in constructing regular graphs of given girth

Graphs and digraphs with all 2-factors isomorphic

g

A family of regular graphs of girth 5

and minimum order. We focus on girth

Regular bipartite graphs with all 2-factors isomorphic

g=5

On minimally one-factorable r -regular bipartite graphs

, where cages are known only for degrees

Pseudo 2-factor isomorphic regular bipartite graphs

k \le 7

Characterizing minimally 1-factorable r-regular bipartite graphs

. We construct regular graphs of girth

On 3-cut reductions of minimally 1-factorable cubic bigraphs

5

Veronese Varieties Over Finite Fields and Their Projections

using techniques exposed by Funk [Note di Matematica. 29 suppl.1, (2009) 91 - 114] and Abreu et al. [Discrete Math. 312 (2012), 2832 - 2842] to obtain the best upper bounds known hitherto. The tables given in the introduction show the improvements obtained with our results.