Helly property associated with the discrete planes.
Hypergraph systems and their extensions
Hypergraphs and intervals
Hypergraphs and intervals. II.
Hypergraphs and intervals. III.
Hypergraphs with large transversal number and with edge sizes at least four
Let H be a hypergraph on n vertices and m edges with all edges of size at least four. The transversal number τ(H) of H is the minimum number of vertices that intersect every edge. Lai and Chang [An upper bound for the transversal numbers of 4-uniform hypergraphs, J. Combin. Theory Ser. B, 1990, 50(1), 129–133] proved that τ(H) ≤ 2(n+m)/9, while Chvátal and McDiarmid [Small transversals in hypergraphs, Combinatorica, 1992, 12(1), 19–26] proved that τ(H) ≤ (n + 2m)/6. In this paper, we characterize...
Hypergraphs with Pendant Paths are not Chromatically Unique
In this note it is shown that every hypergraph containing a pendant path of length at least 2 is not chromatically unique. The same conclusion holds for h-uniform r-quasi linear 3-cycle if r ≥ 2.
Improved bounds for radio -chromatic number of hypercube .
Locally tree-like graphs
Loose Hamilton cycles in random 3-uniform hypergraphs.
Loose Hamilton cycles in random uniform hypergraphs.
Marginalization in models generated by compositional expressions
In the framework of models generated by compositional expressions, we solve two topical marginalization problems (namely, the single-marginal problem and the marginal-representation problem) that were solved only for the special class of the so-called “canonical expressions”. We also show that the two problems can be solved “from scratch” with preliminary symbolic computation.
Maximal hypergraphs with respect to the bounded cost hereditary property
The hereditary property of hypergraphs generated by the cost colouring notion is considered in the paper. First, we characterize all maximal graphs with respect to this property. Second, we give the generating function for the sequence describing the number of such graphs with the numbered order. Finally, we construct a maximal hypergraph for each admissible number of vertices showing some density property. All results can be applied to the problem of information storage.
Maximale stabile Punktmengen und minimale Überdeckungen gleichgewichtiger Hypergrraphen.
Maximizing Spectral Radii of Uniform Hypergraphs with Few Edges
In this paper we investigate the hypergraphs whose spectral radii attain the maximum among all uniform hypergraphs with given number of edges. In particular we characterize the hypergraph(s) with maximum spectral radius over all unicyclic hypergraphs, linear or power unicyclic hypergraphs with given girth, linear or power bicyclic hypergraphs, respectively.
Maximum Hypergraphs without Regular Subgraphs
We show that an n-vertex hypergraph with no r-regular subgraphs has at most 2n−1+r−2 edges. We conjecture that if n > r, then every n-vertex hypergraph with no r-regular subgraphs having the maximum number of edges contains a full star, that is, 2n−1 distinct edges containing a given vertex. We prove this conjecture for n ≥ 425. The condition that n > r cannot be weakened.
More constructions for Turan's (3,4)-conjecture.
Neochromatica
We create and discuss several modifications to traditional graph coloring. In particular, we classify various notions of coloring in a proper hierarchy. We concentrate on grid graphs whose colorings can be represented by natural number entries in arrays with various restrictions.
Neue ergebnisse der theorie der hypergraphen mit anwendungen in der informationtheorie.
Niche Hypergraphs
If D = (V,A) is a digraph, its niche hypergraph NH(D) = (V, E) has the edge set ℇ = {e ⊆ V | |e| ≥ 2 ∧ ∃ v ∈ V : e = N−D(v) ∨ e = N+D(v)}. Niche hypergraphs generalize the well-known niche graphs (see [11]) and are closely related to competition hypergraphs (see [40]) as well as double competition hypergraphs (see [33]). We present several properties of niche hypergraphs of acyclic digraphs.