On the discrepancy of coloring finite sets.
On the discrepancy of quasi-progressions.
On the Hypercompetition Numbers of Hypergraphs with Maximum Degree at Most Two
In this note, we give an easy and short proof for the theorem by Park and Kim stating that the hypercompetition numbers of hypergraphs with maximum degree at most two is at most two.
On the rainbow connection of Cartesian products and their subgraphs
Rainbow connection number of Cartesian products and their subgraphs are considered. Previously known bounds are compared and non-existence of such bounds for subgraphs of products are discussed. It is shown that the rainbow connection number of an isometric subgraph of a hypercube is bounded above by the rainbow connection number of the hypercube. Isometric subgraphs of hypercubes with the rainbow connection number as small as possible compared to the rainbow connection of the hypercube are constructed....
On the size of minimal unsatisfiable formulas.
On the upper and lower chromatic numbers of BSQSs(16).
On total matching numbers and total covering numbers for -uniform hypergraphs
On tours that contain all edges of a hypergraph.
On uniquely partitionable relational structures and object systems
We introduce object systems as a common generalization of graphs, hypergraphs, digraphs and relational structures. Let C be a concrete category, a simple object system over C is an ordered pair S = (V,E), where E = A₁,A₂,...,Aₘ is a finite set of the objects of C, such that the ground-set of each object is a finite set with at least two elements and . To generalize the results on graph colourings to simple object systems we define, analogously as for graphs, that an additive induced-hereditary...
One More Turán Number and Ramsey Number for the Loose 3-Uniform Path of Length Three
Let P denote a 3-uniform hypergraph consisting of 7 vertices a, b, c, d, e, f, g and 3 edges {a, b, c}, {c, d, e}, and {e, f, g}. It is known that the r-color Ramsey number for P is R(P; r) = r + 6 for r ≤ 9. The proof of this result relies on a careful analysis of the Turán numbers for P. In this paper, we refine this analysis further and compute the fifth order Turán number for P, for all n. Using this number for n = 16, we confirm the formula R(P; 10) = 16.
Optimal Betti numbers of forest ideals.
Packing of nonuniform hypergraphs - product and sum of sizes conditions
Hypergraphs of order n are mutually packable if one can find their edge disjoint copies in the complete hypergraph of order n. We prove that two hypergraphs are mutually packable if the product of their sizes satisfies some upper bound. Moreover we show that an arbitrary set of the hypergraphs is mutually packable if the sum of their sizes is sufficiently small.
Packing the Hypercube
Let G be a graph that is a subgraph of some n-dimensional hypercube Qn. For sufficiently large n, Stout [20] proved that it is possible to pack vertex- disjoint copies of G in Qn so that any proportion r < 1 of the vertices of Qn are covered by the packing. We prove an analogous theorem for edge-disjoint packings: For sufficiently large n, it is possible to pack edge-disjoint copies of G in Qn so that any proportion r < 1 of the edges of Qn are covered by the packing.
Pattern hypergraphs.
Platonic hypermaps.
Quantum field theory over .
Rainbow -factors of complete -uniform -partite hypergraphs.
Ramsey theorem for classes of hypergraphs with forbidden complete subhypergraphs
Real time asymptotic packing.
Regular societies without short cycles