The number of Hamiltonian decompositions of regular graphs

DOI10.1007/s11856-017-1583-yzbMath1400.05139arXiv1512.07655OpenAlexW2963248084MaRDI QIDQ1686305

Roman Glebov, Zur Luria, Benjamin Sudakov

Publication date: 21 December 2017

Published in: Israel Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1512.07655

zbMATH Keywords

Hamiltonian cycleregular graphHamiltonian decomposition

Mathematics Subject Classification ID

Enumeration in graph theory (05C30) Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.) (05C70) Eulerian and Hamiltonian graphs (05C45) Graph designs and isomorphic decomposition (05C51)

Related Items (4)

Number of 1-factorizations of regular high-degree graphs ⋮ Hamiltonian decomposition and verifying vertex adjacency in 1-skeleton of the traveling salesperson polytope by variable neighborhood search ⋮ Hamiltonian cycles above expectation in \(r\)-graphs and quasi-random \(r\)-graphs ⋮ Backtracking Algorithms for Constructing the Hamiltonian Decomposition of a 4-regular Multigraph

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Counting and packing Hamilton cycles in dense graphs and oriented graphs
• On the number of Hamilton cycles in pseudo-random graphs
• Hamiltonian cycles in Dirac graphs
• Maximizing Hamiltonian pairs and \(k\)-sets via numerous leaves in a tree
• Hamiltonian decomposition of Cayley graphs of degree 4
• Hamiltonian circuits in random graphs
• On the number of perfect matchings and Hamilton cycles in \(\varepsilon\)-regular non-bipartite graphs
• On packing Hamilton cycles in \(\varepsilon\)-regular graphs
• Random matchings which induce Hamilton cycles and Hamiltonian decompositions of random regular graphs
• Hamilton decompositions of regular expanders: A proof of Kelly's conjecture for large tournaments
• The maximum number of Hamiltonian paths in tournaments
• Hamilton decompositions of regular expanders: applications
• Über drei kombinatorische Probleme am \(n\)-dimensionalen Würfel und Würfelgitter
• Local resilience of graphs
• The Numbers of Spanning Trees, Hamilton Cycles and Perfect Matchings in a Random Graph
• Edge-disjoint Hamilton cycles in random graphs
• Proof of the 1-factorization and Hamilton Decomposition Conjectures
• On the Number of Hamilton Cycles in Sparse Random Graphs

This page was built for publication: The number of Hamiltonian decompositions of regular graphs