Marien Abreu

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Main talks 1. Simeon Ball, On subsets of a finite vector space in which every subset of basis size is a basis 2. Simon Blackburn, Honeycomb arrays 3. Gàbor Korchmàros, Curves over finite fields, an approach from finite geometry 4. Cheryl Praeger, Basic pregeometries 5. Bernhard Schmidt, Finiteness of circulant weighing matrices of fixed weight 6. Douglas(More)
Let k, l,m, n, and μ be positive integers. A Zμ-scheme of valency (k, l) and order (m,n) is an m × n array (Sij) of subsets Sij ⊆ Zμ such that for each row and column one has ∑n j=1 |Sij | = k and ∑m i=1 |Sij | = l, respectively. Any such scheme is an algebraic equivalent of a (k, l)-semiregular bipartite voltage graph with n and m vertices in the(More)
We show that a digraph which contains a directed 2-factor and has minimum in-degree and out-degree at least four has two non-isomorphic directed 2-factors. As a corollary we deduce that every graph which contains a 2factor and has minimum degree at least eight has two non-isomorphic 2factors. In addition we construct: an infinite family of strongly(More)
A bipartite graph is pseudo 2–factor isomorphic if all its 2–factors have the same parity of number of circuits. In a previous paper we have proved that pseudo 2–factor isomorphic k–regular bipartite graphs exist only for k ≤ 3, and partially characterized them. In particular we proved that the only essentially 4–edge-connected pseudo 2–factor isomorphic(More)
Configurations of type (κ +1)κ give rise to κ–regular simple graphs via configuration graphs. On the other hand, neighbourhood geometries of C4–free κ–regular simple graphs on κ 2 + 1 vertices turn out to be configurations of type (κ + 1)κ. We investigate which configurations of type (κ +1)κ are equal or isomorphic to the neighbourhood geometry of their(More)
In this paper we obtain (q + 3)–regular graphs of girth 5 with fewer vertices than previously known ones for q = 13, 17, 19 and for any prime q ≥ 23 performing operations of reductions and amalgams on the Levi graph Bq of an elliptic semiplane of type C. We also obtain a 13–regular graph of girth 5 on 236 vertices from B11 using the same technique.