Mathematics

"Reductio ad absurdum, which Euclid loved so much,
is one of a mathematician's finest weapons. It is
far finer than any chess gambit: a chess player
may offer the sacrifice of a pawn or even a piece,
but a mathematician offers the game."
G.H.Hardy

My research areas:

structural graph theory, graph minors, coloring of graphs, blocking sets, complete caps over GF(3), Hamiltonian cycles in regular graphs

Also interested in:

matroid theory, combinatorial geometry, games

Publications:

On complete caps in the projective geometries over F_3. (with R.Hill, I.Landjev, C.Jones and L.Storme). Journal of Geometry, Vol.67 (2000), 127-144.
Operations which preserve path-width at most two. (with P.Hajnal). Combinatorics Probability and Computing, 10 (2001), 277-291.
The Arc-Width of a Graph. (with P.Hajnal). The Electronic Journal of Combinatorics, 8 (2001), R34.
Minimal blocking sets in PG(2,8) and maximal partial spreads in PG(3,8). (with A.Del Fra, S.Innamorati, L.Storme). Designs, Codes and Cryptography, Volume 31 issue 1, (2004), 15-26.
Largest minimal blocking sets in PG(2,8). (with S. Innamorati). Journal of Combinatorial Designs, Vol.11. Issue 3, (2003) 162-169.
Partitioning the positive integers to seven Beatty sequences. (with P.P.Varjú). Indagationes Mathematicae, 14 (2), (2003) 149-161.
Multiple blocking sets in PG(n,q), n>=3. (with L.Storme). Designs, Codes and Cryptography, 33 August (2004), 5-21.
On complete caps in the projective geometries over F_3 II: New improvements. (with Y.Edel, R.Hill, L.Storme). Journal of Combinatorial Mathematics and Combinatorial Computing, 49, (2004), 9-31.
Note on disjoint blocking sets in Galois planes. (with S.Marcugini, F.Pambianco and T.Szőnyi). Journal of Combinatorial Designs, Volume 14, Issue 2 (March 2006) 149-158.
A contribution to queens graphs: a substitution method. (with G.Ambrus). Discrete Mathematics, 306 (2006) 1105-1114.
A contribution to infinite disjoint covering systems. (with P.P.Varjú). Journal de Théorie des Nombres de Bordeaux, 17 no.1.(2005), 51-55.
Directed path-width and monotonicity in digraph searching. Graphs and Combinatorics, 22 (2006) No. 2, 161-172.
Bounded-Degree Graphs have Arbitrarily Large Geometric Thickness. (with J.Matousek and D.Wood). The Electronic Journal of Combinatorics, 13 (2006), R#3.
Claw-decompositions and Tutte-orientations (with C.Thomassen) Journal of Graph Theory, 52 (2006), 135-146.
The slope parameter of graphs (with G.Ambrus and P.Hajnal). Acta Scientiarum Mathematicarum 72 (2006), 875-889.
On square-free edge colorings of graphs (with P.P.Varjú). Ars Combinatoria 87 (2008), 377-383.
On square-free vertex colorings of graphs (with P.P.Varjú). Studia Scientiarum Mathematicarum Hungarica 44 (2007), 411-422.
Notes on nonrepetitive graph colouring (with D.R.Wood). Electronic Journal of Combinatorics 15 (2008), Research Paper 99, 13 pp.
What is on his mind? (with M.Kriesell). Discrete Mathematics 310(20) (2010), 2573-2583.
On winning Fast in Avoider-Enforcer Games (with M.Stojakovic). Electronic Journal of Combinatorics 17 (2010), Research Paper 56, 12 pp.
Towards the Albertson Conjecture (with G.Tóth). Electronic Journal of Combinatorics 17 (2010), Research Paper 73, 15 pp.
Elementary proof techniques for the maximum number of islands. (with P.Hajnal and E.K.Horváth). European Journal of Combinatorics 32 (2011), 276-281.