Hamilton cycles and paths in vertex-transitive graphs-current directions

DOI10.1016/j.disc.2009.02.017zbMath1229.05178DBLPjournals/dm/KutnarM09OpenAlexW2016348586WikidataQ64384701 ScholiaQ64384701MaRDI QIDQ1044917

Klavdija Kutnar, Dragan Marušič

Publication date: 15 December 2009

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

Full work available at URL: https://doi.org/10.1016/j.disc.2009.02.017

zbMATH Keywords

Cayley graphHamilton pathvertex-transitive graphHamilton cyclesemiregularimprimitive

Mathematics Subject Classification ID

Research exposition (monographs, survey articles) pertaining to combinatorics (05-02) Paths and cycles (05C38) Graphs and abstract algebra (groups, rings, fields, etc.) (05C25) Eulerian and Hamiltonian graphs (05C45)

Related Items (16)

On a Combinatorial Generation Problem of Knuth ⋮ Loopless algorithms to generate maximum length Gray cycles wrt. \(k\)-character substitutions ⋮ On generalizations of the Petersen graph and the Coxeter graph ⋮ Hamilton paths in vertex-transitive graphs of order \(10p\) ⋮ Hamilton cycles in dense vertex-transitive graphs ⋮ Hamiltonian cycles in Cayley graphs of imprimitive complex reflection groups ⋮ Fault-free mutually independent Hamiltonian cycles of faulty star graphs ⋮ Resolving the Hamiltonian problem for vertex-transitive graphs of order a product of two primes ⋮ What is on his mind? ⋮ Hamiltonian cycles in covering graphs of trees ⋮ Polynomials of degree 4 over finite fields representing quadratic residues ⋮ Proof of the middle levels conjecture ⋮ Hamiltonicity of 3-arc graphs ⋮ Hamilton cycles in primitive vertex-transitive graphs of order a product of two primes – the case PSL(2, q^2) acting on cosets of PGL(2, q) ⋮ Vertex-transitive digraphs of order \(p^5\) are Hamiltonian ⋮ Vertex-transitive graphs that have no Hamilton decomposition

Cites Work

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• Hamiltonian cycles in vertex symmetric graphs of order \(2p^ 2\)
• A class of non-Cayley vertex-transitive graphs associated with PSL(2,\(p\))
• Cayley digraphs of prime-power order are hamiltonian
• Minimal normal subgroups of transitive permutation groups of square-free degree
• Semiregular automorphisms of vertex-transitive graphs of certain valencies
• The Hamilton spaces of Cayley graphs on abelian groups
• Lifting Hamilton cycles of quotient graphs
• Connected graphs as subgraphs of Cayley graphs: conditions on hamiltonicity
• On hamiltonicity of circulant digraphs of outdegree three
• Hamilton paths and cycles in vertex-transitive graphs of order \(6p\)
• Mutually independent Hamiltonian cycles for the pancake graphs and the star graphs
• Hamiltonian cycles in (2,3,c)-circulant digraphs
• Hamiltonian paths in Cayley graphs
• Hamiltonian paths in vertex-symmetric graphs of order 4p
• Hamiltonian circuits in Cayley graphs
• The classification of Hamiltonian generalized Petersen graphs
• Connected Cayley graphs of semi-direct products of cyclic groups of prime order by Abelian groups are Hamiltonian
• On edge-Hamiltonian property of Cayley graphs
• A Hamilton cycle in the Cayley graph of the \(\langle 2,p,3 \rangle\) presentation of PSL\(_ 2(p)\)
• On vertex symmetric digraphs
• On hamiltonian circuits in Cayley diagrams
• Hamiltonian paths in vertex-symmetric graphs of order 5p
• A method in graph theory
• Generating all graph coverings by permutation voltage assignments
• Permutation groups, vertex-transitive digraphs and semiregular automorphisms
• Classifying vertex-transitive graphs whose order is a product of two primes
• On Hamiltonicity of vertex-transitive graphs and digraphs of order \(p^4\)
• Advances on the Hamiltonian problem -- a survey
• \(s\)-regular cyclic coverings of the three-dimensional hypercube \(Q_{3}\).
• Automorphism groups with cyclic commutator subgroup and Hamilton cycles
• On a generalization of Chvátal's condition giving new Hamiltonian degree sequences
• Gray codes for reflection groups
• On a class of Hamiltonian laceable 3-regular graphs
• Hamiltonian cycles and paths in Cayley graphs and digraphs---a survey
• Hamiltonicity of vertex-transitive graphs of order 4\(p\)
• Hamiltonicity of cubic Cayley graphs
• On Hamilton's ideals
• Cayley maps
• Long cycles in vertex-transitive graphs
• Transitive Permutation Groups Without Semiregular Subgroups
• Note on Hamilton Circuits
• A graph which is edge transitive but not arc transitive
• On Hamiltonian Cycles in Metacirculant Graphs
• Hamilton cycles in regular graphs
• QUASIPRIMITIVE GROUPS WITH NO FIXED POINT FREE ELEMENTS OF PRIME ORDER
• Sparse pseudo‐random graphs are Hamiltonian
• New Constructions of Groups Without Semiregular Subgroups
• Point-symmetric graphs with a prime number of points
• HOW TO DESCRIBE A GRAPH
• Tilings of the Torus and the Klein Bottle and Vertex-Transitive Graphs on a Fixed Surface
• Some Theorems on Abstract Graphs
• A survey: Hamiltonian cycles in Cayley graphs
• Hamilton-connected Cayley graphs on Hamiltonian groups
• Research problems

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