output
19932026
Showing 2015 · math.COShow all

10 papers · 2 filters

math.CO2015

Constructing minimal blocking sets using field reduction

Geertrui Van de Voorde

We present a construction for minimal blocking sets with respect to -spaces in , the -dimensional projective space over the finite field $\mathb…

math.CO2015★ 25 cited

A linear set view on KM-arcs

Maarten De Boeck, Geertrui Van de Voorde

In this paper, we study KM-arcs of type t, i.e. point sets of size q + t in PG(2, q) such that every line contains 0, 2 or t of its points. We use field reduction to give a differe…

math.CO2015★ 17 cited

Generation of cubic graphs and snarks with large girth

Gunnar Brinkmann, Jan Goedgebeur

We describe two new algorithms for the generation of all non-isomorphic cubic graphs with girth at least which are very efficient for and show how these alg…

math.CO2015

Necessary conditions for the existence of 3-designs over finite fields with nontrivial automorphism groups

Maarten De Boeck, Anamari Nakic

A q-design with parameters t-(v,k,lambda_t)_q is a pair (V, B) of the v-dimensional vector space V over GF(q) and a collection B of k-dimensional subspaces of V, such that each t-d…

math.CO2015★ 2 cited

Exhaustive generation of -critical -free graphs

Jan Goedgebeur, Oliver Schaudt

We describe an algorithm for generating all -critical -free graphs, based on a method of Hoàng et al. Using this algorithm, we prove that there are only finitely man…

math.CO2015

On the spectrum of sizes of semiovals contained in the Hermitian curve

Daniele Bartoli, Gyorgy Kiss, Stefano Marcugini +1

Some constructions and bounds on the sizes of semiovals contained in the Hermitian curve are given. A construction of an infinite family of 2-blocking sets of the Hermitian curve i…

math.CO2015

Dimensional dual hyperovals in classical polar spaces

John Sheekey

In this paper we show that n-dimensional dual hyperovals cannot exist in all but one classical polar space of rank n if n is even. This resolves a question posed by Yoshiara.

math.CO2015★ 5 cited

Obstructions for three-coloring graphs without induced paths on six vertices

Maria Chudnovsky, Jan Goedgebeur, Oliver Schaudt +1

We prove that there are 24 4-critical -free graphs, and give the complete list. We remark that, if is connected and not a subgraph of , there are infinitely many 4-cr…

math.CO2015★ 8 cited

On semi-finite hexagons of order containing a subhexagon

Anurag Bishnoi, Bart De Bruyn

The research in this paper was motivated by one of the most important open problems in the theory of generalized polygons, namely the existence problem for semi-finite thick genera…

math.CO2015★ 22 cited

Recursive generation of IPR fullerenes

Jan Goedgebeur, Brendan D. McKay

We describe a new construction algorithm for the recursive generation of all non-isomorphic IPR fullerenes. Unlike previous algorithms, the new algorithm stays entirely within the…