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Every 4-connected graph with crossing number 2 is Hamiltonian. (English) Zbl 1401.05175

Summary: A seminal theorem of Tutte states that 4-connected planar graphs are Hamiltonian. Applying a result of R. Thomas and X. Yu [J. Comb. Theory, Ser. B 62, No. 1, 114–132 (1994; Zbl 0802.05051)], one can show that every 4-connected graph with crossing number 1 is Hamiltonian. In this paper, we continue along this path and prove the titular statement. We also discuss the traceability and Hamiltonicity of 3-connected graphs with small crossing number and few 3-cuts, and present applications of our results.

MSC:

05C45 Eulerian and Hamiltonian graphs
05C10 Planar graphs; geometric and topological aspects of graph theory
05C38 Paths and cycles

Citations:

Zbl 0802.05051
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References:

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