Péter Hajnal

Partition of graphs with condition on the connectivity and minimum degree

C. Thomassen and M. Szegedy proved the existence of a functionf(s, t) such that the points of anyf(s, t)-connected graph have a decomposition into two non-empty sets such that the subgraphs induced by them ares-connected andt-connected, respectively. We prove, thatf(s, t) ≦ 4s+4t − 13 and examine a similar problem for the minimum degree.

Elementary proof techniques for the maximum number of islands

Islands are combinatorial objects that can be intuitively defined on a board consisting of a finite number of cells. It is a fundamental property that two islands are either containing or disjoint. Czedli determined the maximum number of rectangular islands. Pluhar solved the same problem for bricks, and Horvath, Nemeth and Pluhar for triangular islands. Here, we give a much shorter proof for these results, and also for new, analogous results on toroidal and some other boards.

On packing bipartite graphs

AbstractG andH, two simple graphs, can be packed ifG is isomorphic to a subgraph of

Simply sequentially additive labelings of 2-regular graphs

\overline H

Saturated Simple and 2-simple Topological Graphs with Few Edges

, the complement ofH. A theorem of Catlin, Spencer and Sauer gives a sufficient condition for the existence of packing in terms of the product of the maximal degrees ofG andH. We improve this theorem for bipartite graphs. Our condition involves products of a maximum degree with an average degree. Our relaxed condition still guarantees a packing of the two bipartite graphs.

Partition problems and kernels of graphs

The

Combinatorial Properties of Poly-Bernoulli Relatives

{\mathbb B}_n^{(k)}

ON THE STRUCTURE OF GRAPHS WITH PATH-WIDTH AT MOST TWO

poly-Bernoulli numbers --- a natural generalization of classical Bernoulli numbers (