Hall's theorem for hypergraphs

Author: emsc

August undefined, 2024

WebOn a criterion for matching in hypergraphs. Graphs and Combinatorics9, 209–212 (1993) Google Scholar Aharoni, R., Kessler, O.: On a possible extension of Hall's theorem to … WebJun 29, 2024 · At Gil Kalai's blog, Hall’s theorem for hypergraphs (Ron Aharoni and Penny Haxell, 1999) is given, and then it says, "Ron Aharoni and Penny Haxell described special type of triangulations, and then miraculously deduced their theorem from Sperner’s lemma.

A generalization of hall

WebAbstract In this paper we prove a generalized version of Hall's theorem in graphs‎, ‎for hypergraphs‎. More precisely‎, ‎let $\mathcal {H}$ be a $k$-uniform $k$-partite hypergraph with some... Webgraph, when nis su ciently large; this generalises a theorem of Nikiforov who proved stronger results in the case = 2. We also obtain an -spectral version of the Erd}os-Ko-Rado theorem on t-intersecting k-uniform hypergraphs. 1 Introduction Let Fbe a family of k-uniform hypergraphs. A hypergraph His F-free if for every F2F, highest rated suvs 2014

Hypergraph regularity and the multidimensional Szemerédi theorem ...

WebSep 24, 2015 · Theorem, and the deﬁciency version of Hall’s Theorem in several graph and hypergraph classes, including bipartite and K˝ onig-Egerv´ ary graphs, as well as balanced and normal hypergraphs. WebBy a hypergraph we mean a pair (V,A), where V is a finite set, and A = {A 1,…,A m} is a family of its different subsets. V means the number 1 m of elements of V; this is usually … WebDec 18, 2024 · We also obtain some simple results in case \mathcal {F} itself is a graph-based hypergraph (for example \mathcal {F} is a specific Berge copy of a graph F_0 ). Recall that the expansion F_0^ {+k} of a graph F_0 is the Berge copy of F_0 which is constructed by adding k-2 new and distinct vertices to each edge of F_0. highest rated suvs 2023

Extremal Problems for Hypergraphs SpringerLink

WebOne version of Ramsey’s theorem states that, for any sand t, there is a natural number nsuch that, in any 2-colouring of the edges of the complete graph K ... os-Hajnal theorem to tripartite 3-uniform hypergraphs. In any given 3-uniform hypergraph on nvertices, one may always nd a complete or empty tripartite subgraph with parts of order at ... WebThe statements and proofs of the core version of the containers theorem originally appeared in [1, Proposition 3.1] and [12, Theorem 3.4]. We state it here as Theorem8. Our main result is a new proof of this theorem, whose advantages are described below. Our proof. All previously known proofs of the containers theorem are based on the so- highest rated sweep money market fundsWebA GENERALIZATION OF HALL’S THEOREM FOR k-UNIFORM k-PARTITE HYPERGRAPHS REZA JAFARPOUR-GOLZARI Abstract. In this paper we prove a … highest rated sweepstakes sites online

"In the mathematical field of graph theory, Hall-type theorems for hypergraphs are several generalizations of Hall's marriage theorem from graphs to hypergraphs. Such theorems were proved by Ofra Kessler, Ron Aharoni, Penny Haxell, Roy Meshulam, and others. See more Hall's marriage theorem provides a condition guaranteeing that a bipartite graph (X + Y, E) admits a perfect matching, or - more generally - a matching that saturates all vertices of Y. The condition involves the number of See more A transversal (also called vertex-cover or hitting-set) in a hypergraph H = (V, E) is a subset U of V such that every hyperedge in E contains at least one vertex of U. The smallest size of a transversal in H is denoted by τ(H). Let H = (X + Y, E) … See more In abstract simplicial complexes Let V be a set of vertices. Let C be an abstract simplicial complex on V. Let Vy (for y in Y) be subsets of V. A C-V-transversal is … See more Hall's condition requires that, for each subset Y0 of Y, the set of neighbors of Y0 is sufficiently large. With hypergraphs this condition is … See more Let H = (X + Y, E) be a bipartite hypergraph (as defined in 1. above), in which the size of every hyperedge is exactly r, for some integer r > 1. Suppose that, for every … See more We say that a set K of edges pins another set F of edges if every edge in F intersects some edge in K. The width of a hypergraph H = (V, E), denoted w(H), is the smallest size of a subset of … See more A rainbow matching is a matching in a simple graph, in which each edge has a different "color". By treating the colors as vertices in the set … See more " - Hall's theorem for hypergraphs

A generalization of hall

Hypergraph regularity and the multidimensional Szemerédi theorem ...

Hall's theorem for hypergraphs

Did you know?