The 11-element case of Frankl's conjecture.
The integer sequence A002620 and upper antagonistic functions.
The intersection structure of -intersecting families.
The Least Eigenvalue of Graphs whose Complements Are Uni- cyclic
A graph in a certain graph class is called minimizing if the least eigenvalue of its adjacency matrix attains the minimum among all graphs in that class. Bell et al. have identified a subclass within the connected graphs of order n and size m in which minimizing graphs belong (the complements of such graphs are either disconnected or contain a clique of size n/2 ). In this paper we discuss the minimizing graphs of a special class of graphs of order n whose complements are connected and contains...
The structure of maximal zero-sum free sequences
The structure of maximum subsets of with no solutions to .
The Turán density of the hypergraph .
The Turán problem for hypergraphs on fixed size.
Three-and-more set theorems
In this paper we generalize classical 3-set theorem related to stable partitions of arbitrary mappings due to Erdős-de Bruijn, Katětov and Kasteleyn. We consider a structural generalization of this result to partitions preserving sets of inequalities and characterize all finite sets of such inequalities which can be preserved by a “small” coloring. These results are also related to graph homomorphisms and (oriented) colorings.
Towards a Katona type proof for the 2-intersecting Erdős-Ko-Rado theorem.
Traces of uniform families of sets.
Traces without maximal chains.
Triangle-intersecting families of graphs
Turán number of two vertex-disjoint copies of cliques
The Turán number of a given graph , denoted by , is the maximum number of edges in an -free graph on vertices. Applying a well-known result of Hajnal and Szemerédi, we determine the Turán number ) of a vertex-disjoint union of cliques and for all values of .