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.
Hyperidentities in transitive graph algebras
Graph algebras establish a connection between directed graphs without multiple edges and special universal algebras of type (2,0). We say that a graph G satisfies an identity s ≈ t if the corresponding graph algebra A(G) satisfies s ≈ t. A graph G = (V,E) is called a transitive graph if the corresponding graph algebra A(G) satisfies the equation x(yz) ≈ (xz)(yz). An identity s ≈ t of terms s and t of any type t is called a hyperidentity of an algebra A̲ if whenever the operation symbols occurring...
Hyperoctahedral species.
Hyperplane Arrangements with a Lattice of Regions.
Hyperplane Coverings and Blocking Sets.
Hyperplanes in matroids and the axiom of choice
We show that in set theory without the axiom of choice ZF, the statement sH: “Every proper closed subset of a finitary matroid is the intersection of hyperplanes including it” implies AC, the axiom of choice for (nonempty) finite sets. We also provide an equivalent of the statement AC in terms of “graphic” matroids. Several open questions stay open in ZF, for example: does sH imply the axiom of choice?
Hypersymmetric functions and Pochhammers of nonautonomous matrices.
Hypo-Eulerian and Hypo-Traversable Graphs.