TY - JOUR
AB - We give several results showing that different discrete structures typically gain certain spanning substructures (in particular, Hamilton cycles) after a modest random perturbation. First, we prove that adding linearly many random edges to a dense k-uniform hypergraph ensures the (asymptotically almost sure) existence of a perfect matching or a loose Hamilton cycle. The proof involves an interesting application of Szemerédi's Regularity Lemma, which might be independently useful. We next prove that digraphs with certain strong expansion properties are pancyclic, and use this to show that adding a linear number of random edges typically makes a dense digraph pancyclic. Finally, we prove that perturbing a certain (minimum-degree-dependent) number of random edges in a tournament typically ensures the existence of multiple edge-disjoint Hamilton cycles. All our results are tight.
AU - Krivelevich, Michael
AU - Kwan, Matthew Alan
AU - Sudakov, Benny
ID - 9575
JF - Electronic Notes in Discrete Mathematics
SN - 1571-0653
TI - Cycles and matchings in randomly perturbed digraphs and hypergraphs
VL - 49
ER -