On systems of graphs intersecting in paths
Families of triples with high minimum degree are hamiltonian
In this paper we show that every family of triples, that is, a 3-uniform hypergraph, with minimum degree at least [...] contains a tight Hamiltonian cycle
Atomy ve svazu uniformit
Orthogonal partitions and covering of graphs
On classes of graphs determined by forbidden subgraphs
More on the complexity of cover graphs
In response to [3] and [4] we prove that the recognition of cover graphs of finite posets is an NP-hard problem.
On number of covering arcs in orderings
On generating of relations
Partite construction and Ramseyan theorems for sets, numbers and spaces
Large trees in random graphs
Partitions of vertices
Van der Waerden theorem for sequences of integers not containing an arithmetic progression of terms
Note on the number of monoids of order
On Ramsey graphs without cycles of short odd lengths
Ramsey theorem for classes of hypergraphs with forbidden complete subhypergraphs
Note on Ramsey numbers and self-complementary graphs
Arithmetic progressions of length three in subsets of a random set
Metric spaces with point character equal to their size
In this paper we consider the point character of metric spaces. This parameter which is a uniform version of dimension, was introduced in the context of uniform spaces in the late seventies by Jan Pelant, Cardinal reflections and point-character of uniformities, Seminar Uniform Spaces (Prague, 1973–1974), Math. Inst. Czech. Acad. Sci., Prague, 1975, pp. 149–158. Here we prove for each cardinal , the existence of a metric space of cardinality and point character . Since the point character can...
Ramsey Properties of Random Graphs and Folkman Numbers
For two graphs, G and F, and an integer r ≥ 2 we write G → (F)r if every r-coloring of the edges of G results in a monochromatic copy of F. In 1995, the first two authors established a threshold edge probability for the Ramsey property G(n, p) → (F)r, where G(n, p) is a random graph obtained by including each edge of the complete graph on n vertices, independently, with probability p. The original proof was based on the regularity lemma of Szemerédi and this led to tower-type dependencies between...
On generalized shift graphs
In 1968 Erdős and Hajnal introduced shift graphs as graphs whose vertices are the k-element subsets of [n] = 1,...,n (or of an infinite cardinal κ ) and with two k-sets and joined if . They determined the chromatic number of these graphs. In this paper we extend this definition and study the chromatic number of graphs defined similarly for other types of mutual position with respect to the underlying ordering. As a consequence of our result, we show the existence of a graph with interesting...
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