Counterexample to a conjecture of Aharoni and Korman
Dominic van der Zypen
TL;DR
This paper provides a counterexample disproving a conjecture by Aharoni and Korman that finite-edge hypergraphs always have a strongly minimal cover.
Contribution
It introduces the first known counterexample to the conjecture, challenging previous assumptions in hypergraph theory.
Findings
Counterexample disproves the conjecture
Finite-edge hypergraphs may lack strongly minimal covers
Implications for hypergraph covering theory
Abstract
Ron Aharoni and Vladimir Korman conjectured that any hypergraph with only finite edges has a strongly minimal cover. We present a counterexample.
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Taxonomy
TopicsLimits and Structures in Graph Theory · Advanced Graph Theory Research · Graph theory and applications