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- W2535840617 abstract "Abstract A Hamilton Berge cycle of a hypergraph on n vertices is an alternating sequence ( v 1 , e 1 , v 2 , … , v n , e n ) of distinct vertices v 1 , … , v n and distinct hyperedges e 1 , … , e n such that { v 1 , v n } ⊆ e n and { v i , v i + 1 } ⊆ e i for every i ∈ [ n − 1 ] . We prove a Dirac-type theorem for Hamilton Berge cycles in random r-uniform hypergraphs by showing that for every integer r ≥ 3 there exists k = k ( r ) such that for every γ > 0 and p ≥ log k ( r ) ( n ) n r − 1 asymptotically almost surely every spanning subhypergraph H ⊆ H ( r ) ( n , p ) with minimum vertex degree δ 1 ( H ) ≥ ( 1 2 r − 1 + γ ) p ( n − 1 r − 1 ) contains a Hamilton Berge cycle. The minimum degree condition is asymptotically tight and the bound on p is optimal up to possibly the logarithmic factor. As a corollary this gives a new upper bound on the threshold of H ( r ) ( n , p ) with respect to Berge Hamiltonicity." @default.
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- W2535840617 date "2016-10-01" @default.
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- W2535840617 title "A Dirac-type theorem for Hamilton Berge cycles in random hypergraphs" @default.
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- W2535840617 doi "https://doi.org/10.1016/j.endm.2016.09.032" @default.
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