On the Number of Hamilton Cycles in Sparse Random Graphs

DOI10.1137/120884316zbMath1268.05179arXiv1207.2748OpenAlexW2591664023WikidataQ105584146 ScholiaQ105584146MaRDI QIDQ5300478

Michael Krivelevich, Roman Glebov

Publication date: 27 June 2013

Published in: SIAM Journal on Discrete Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1207.2748

zbMATH Keywords

random graphsHamilton cyclesnumber of Hamilton cycles

Mathematics Subject Classification ID

Extremal problems in graph theory (05C35) Random graphs (graph-theoretic aspects) (05C80) Directed graphs (digraphs), tournaments (05C20) Eulerian and Hamiltonian graphs (05C45) Probabilistic methods in extremal combinatorics, including polynomial methods (combinatorial Nullstellensatz, etc.) (05D40)

Related Items (14)

Counting and packing Hamilton cycles in dense graphs and oriented graphs ⋮ The number of Hamiltonian decompositions of regular graphs ⋮ Color‐biased Hamilton cycles in random graphs ⋮ The Threshold Probability for Long Cycles ⋮ Recent advances on the Hamiltonian problem: survey III ⋮ Packing, counting and covering Hamilton cycles in random directed graphs ⋮ Packing and counting arbitrary Hamilton cycles in random digraphs ⋮ Bounding the number of cycles in a graph in terms of its degree sequence ⋮ Packing, counting and covering Hamilton cycles in random directed graphs ⋮ Powers of Hamilton cycles in pseudorandom graphs ⋮ The maximum number of cycles in a graph with fixed number of edges ⋮ Increasing Hamiltonian paths in random edge orderings ⋮ Random directed graphs are robustly Hamiltonian ⋮ Edge Correlations in Random Regular Hypergraphs and Applications to Subgraph Testing

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