Edge reductions in cyclically \(k\)-connected cubic graphs

DOI10.1016/0095-8956(92)90004-HzbMath0711.05030OpenAlexW2038044706MaRDI QIDQ922553

William D. McCuaig

Publication date: 1992

Published in: Journal of Combinatorial Theory. Series B (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0095-8956(92)90004-h

zbMATH Keywords

extremalcyclic connectivityedge reductionk-connected cubic graph

Mathematics Subject Classification ID

Extremal problems in graph theory (05C35) Connectivity (05C40)

Related Items (21)

Graphs with no \(\bar{P}_7\)-minor ⋮ Cyclic connectivity, edge-elimination, and the twisted Isaacs graphs ⋮ The minimality of the Georges–Kelmans graph ⋮ Construction of fullerenes and Pogorelov polytopes with 5-, 6- and one 7-gonal face ⋮ Cyclically five-connected cubic graphs ⋮ A polynomial algorithm determining cyclic vertex connectivity of \(k\)-regular graphs with fixed \(k\) ⋮ A polynomial algorithm determining cyclic vertex connectivity of 4-regular graphs ⋮ Generating \(r\)-regular graphs ⋮ Barnette's conjecture through the lens of the \(Mod_k P\) complexity classes ⋮ The cubic graphs with finite cyclic vertex connectivity larger than girth ⋮ Coverings of cubic graphs and 3-edge colorability ⋮ Edge reductions in cyclically \(k\)-connected cubic graphs ⋮ Topological minors in line graphs -- a proof of Zha's conjecture ⋮ The cyclic edge-connectivity of strongly regular graphs ⋮ Three-dimensional right-angled polytopes of finite volume in the Lobachevsky space: combinatorics and constructions ⋮ The k-conversion number of regular graphs ⋮ A polynomial time algorithm for cyclic vertex connectivity of cubic graphs ⋮ The Nash-Williams conjecture and the dominating cycle conjecture ⋮ Excluded minors in cubic graphs ⋮ Unnamed Item ⋮ The number of removable edges in 3-connected graphs

Cites Work

• Decomposition of 3-connected cubic graphs
• The maximum genus of vertex-transitive graphs
• Edge reductions in cyclically \(k\)-connected cubic graphs
• Construction of class two graphs with maximum vertex degree three
• On generating planar graphs
• Ecken vom Grad \(n\) in minimalen \(n\)-fach zusammenhängenden Graphen
• A non-Hamiltonian planar graph
• Infinite Families of Nontrivial Trivalent Graphs Which are Not Tait Colorable
• A Generation Procedure for the Simple 3-Polytopes With Cyclically 5-Connected Graphs
• On Hamiltonian Circuits
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