On the number of hamiltonian cycles in a maximal planar graph

DOI10.1002/jgt.3190030407zbMath0422.05050OpenAlexW1517929766MaRDI QIDQ3855220

Edward F. Schmeichel, Carsten Thomassen, S. Louis Hakimi

Publication date: 1979

Published in: Journal of Graph Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/jgt.3190030407

zbMATH Keywords

Hamiltonian cyclesminimum numberHamiltonian maximal planar graph

Mathematics Subject Classification ID

Extremal problems in graph theory (05C35) Enumeration in graph theory (05C30) Planar graphs; geometric and topological aspects of graph theory (05C10) Eulerian and Hamiltonian graphs (05C45)

Related Items (11)

Counting Hamiltonian cycles in planar triangulations ⋮ Regular Graphs with Few Longest Cycles ⋮ Hamiltonian Cycles in 4-Connected Planar and Projective Planar Triangulations with Few 4-Separators ⋮ On the maximum number of edges in planar graphs of bounded degree and matching number ⋮ Hamiltonian cycles in 4-connected plane triangulations with few 4-separators ⋮ Hamiltonian properties of polyhedra with few 3-cuts. A survey ⋮ Cycles in 5-connected triangulations ⋮ 4-connected polyhedra have at least a linear number of Hamiltonian cycles ⋮ Types of triangle in Hamiltonian triangulations and an application to domination and k-walks ⋮ Number of Hamiltonian Cycles in Planar Triangulations ⋮ Uniquely Hamiltonian Graphs of Minimum Degree 4

Cites Work

• A theorem on graphs
• Simple paths on polyhedra
• On the number of cycles of lengthk in a maximal planar graph
• Hamiltonian circuits on 3-polytopes

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