2025/04/30 by Bailey, Teegan, Hollars, Isaiah, Li, Yupei +1
#Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.2505.00130
A Berge cycle of length ℓ in a hypergraph H is a sequence of alternating vertices and edges v0e0v1e1...v_ℓ e_ℓ v0 such that \vi,vi+1\⊆ ei for all i, with indices taken modulo ℓ. For n sufficiently large and r≥ \lfloor(n-1)/(2)\rfloor-1 we prove exact minimum degree conditions for an n-vertex, r-uniform hypergraph to contain Berge cycles of every length between 2 and n. In conjunction with previous work, this provides sharp Dirac-type conditions for pancyclicity in r-uniform hypergraphs for all 3≤ r≤ n when n is sufficiently large.