Geodesic
Pósa-type results for Berge hypergraphs
Nika Salia1
1Alfréd Rényi Institute of Mathematics
The electronic journal of combinatorics, Tome 31 (2024) no. 2
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A Berge cycle of length $k$ in a hypergraph $\mathcal H$ is a sequence of distinct vertices and hyperedges $v_1,h_1,v_2,h_2,\dots,v_{k},h_k$ such that $v_{i},v_{i+1}\in h_i$ for all $i\in[k]$, indices taken modulo $k$. F\"uredi, Kostochka and Luo recently gave sharp Dirac-type minimum degree conditions that force non-uniform hypergraphs to have Hamiltonian Berge cycles. We give a sharp Pósa-type lower bound for $r$-uniform and non-uniform hypergraphs that force Hamiltonian Berge cycles.
DOI : 10.37236/11704
Classification : 05C65, 05C45, 05C35
Mots-clés : Hamiltonian cycles, Berge paths, Berge cycles

Nika Salia  1

1 Alfréd Rényi Institute of Mathematics 
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     title = {P\'osa-type results for {Berge} hypergraphs},
     journal = {The electronic journal of combinatorics},
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     doi = {10.37236/11704},
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Nika Salia. Pósa-type results for Berge hypergraphs. The electronic journal of combinatorics, Tome 31 (2024) no. 2. doi: 10.37236/11704

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