On the Minimum Number of Hamiltonian Cycles in Regular Graphs

DOI10.1080/10586458.2017.1306813zbMath1403.05082arXiv1608.00713OpenAlexW2490772428MaRDI QIDQ4646702

Micheal Haythorpe

Publication date: 14 January 2019

Published in: Experimental Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1608.00713

zbMATH Keywords

regular graphsHamiltonian cyclesminimalconstruction

Mathematics Subject Classification ID

Enumeration in graph theory (05C30) Eulerian and Hamiltonian graphs (05C45)

Related Items (5)

Regular Graphs with Few Longest Cycles ⋮ The ratio of the numbers of odd and even cycles in outerplanar graphs ⋮ 4-regular 4-connected Hamiltonian graphs with few Hamiltonian cycles ⋮ Graphs with few hamiltonian cycles ⋮ From one to many rainbow Hamiltonian cycles

Uses Software

• GENREG

Cites Work

• Unnamed Item
• Hamiltonian circuits on the \(n\)-dimensional octahedron
• Independent dominating sets and hamiltonian cycles
• The Planar Hamiltonian Circuit Problem is NP-Complete
• Fast generation of regular graphs and construction of cages
• Non-Sexist Solution of the Menage Problem
• On the Number of Hamilton Cycles in Bounded Degree Graphs
• The Traveling Salesman Problem for Cubic Graphs
• A theorem on tait colorings with an application to the generalized Petersen graphs
• On Hamiltonian Circuits

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