Maximum and minimum toughness of graphs of small genus

DOI10.1016/S0012-365X(96)00238-5zbMath0874.05036OpenAlexW2035440971MaRDI QIDQ1356471

Michael D. Plummer, Henda C. Swart, Wayne Goddard

Publication date: 9 June 1997

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

Full work available at URL: https://doi.org/10.1016/s0012-365x(96)00238-5

zbMATH Keywords

torusextremal graphsplanar graphsconnectivityboundgenustoughness

Mathematics Subject Classification ID

Extremal problems in graph theory (05C35) Planar graphs; geometric and topological aspects of graph theory (05C10) Connectivity (05C40) Eulerian and Hamiltonian graphs (05C45)

Related Items (5)

Robust Connectivity of Graphs on Surfaces ⋮ Hamiltonicity of graphs on surfaces in terms of toughness and scattering number -- a survey ⋮ Toughness in graphs -- a survey ⋮ Unnamed Item ⋮ Bounds for scattering number and rupture degree of graphs with genus

Cites Work

• Toughness and Delaunay triangulations
• An upper bound on the shortness exponent of 1-tough, maximal planar graphs
• Recognizing tough graphs is NP-hard
• Connectivity, genus, and the number of components in vertex-deleted subgraphs
• Uniqueness and faithfulness of embedding of toroidal graphs
• Toughness and nonhamiltonicity of polyhedral graphs
• Das Geschlecht des vollständigen paaren Graphen
• Tough graphs and Hamiltonian circuits.
• Hamiltonian results inK1,3-free graphs
• On the Toughness of a Graph
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