A union-closed family of sets A is a finite collection of sets not all empty such that the union of any two members of A is also a member of A. The following ...
Dec 7, 1998 · An induced subgraph S of a graph G is called a derived subgraph of G if S contains no isolated vertices.
We will show that Conjecture 1, Conjecture 2 are equivalent to the union-closed sets conjecture. ... A graph-theoretic version of the union-closed sets conjecture.
A graph-theoretic version of the union-closed sets conjecture.
A version of the conjecture is also known for hypergraphs, by El-Zahar. [5]. In this paper we give a formulation of the conjecture in the language of graph.
Sep 3, 2024 · The conjecture asserts that in any union-closed family of sets, there exists an element that belongs to at least half of the sets in the family.
ABSTRACT. An induced subgraph S of a graph G is called a derived subgraph of G if S contains no isolated vertices. An edge e of.
A graph-theoretic version of the union-closed sets conjecture · M. El-Zahar · Published in Journal of Graph Theory 1 November 1997 · Mathematics.
Sep 3, 2024 · This paper explores the graph-theoretic formulation of the conjecture and establishes connections between the set-based and graph-based ...
Feb 27, 2022 · We present three new formulations of the union-closed conjecture in terms of matrices, graphs, and hypergraphs. 1 Introduction. The union-closed ...
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