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Longest cycles in 3‐connected hypergraphs and bipartite graphs
Author(s) -
Kostochka Alexandr,
Lavrov Mikhail,
Luo Ruth,
Zirlin Dara
Publication year - 2022
Publication title -
journal of graph theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 54
eISSN - 1097-0118
pISSN - 0364-9024
DOI - 10.1002/jgt.22762
Subject(s) - mathematics , combinatorics , bipartite graph , hypergraph , strong perfect graph theorem , cograph , conjecture , discrete mathematics , hamiltonian path , mathematical proof , edge transitive graph , robertson–seymour theorem , graph , 1 planar graph , line graph , voltage graph , geometry
In the language of hypergraphs, our main result is a Dirac‐type bound: We prove that every 3‐connected hypergraph ℋ with δ ( H ) ≥ max { ∣ V ( H ) ∣ , ∣ E ( H )∣ + 10 4 } has a hamiltonian Berge cycle. This is sharp and refines a conjecture by Jackson from 1981 (in the language of bipartite graphs). Our proofs are in the language of bipartite graphs, since the incidence graph of each hypergraph is bipartite.