an:06989222
Zbl 1401.05175
Ozeki, Kenta; Zamfirescu, Carol T.
Every 4-connected graph with crossing number 2 is Hamiltonian
EN
SIAM J. Discrete Math. 32, No. 4, 2783-2794 (2018).
00415650
2018
j
05C45 05C10 05C38
Hamiltonian cycle; crossing number; 3-cuts
Summary: A seminal theorem of Tutte states that 4-connected planar graphs are Hamiltonian. Applying a result of \textit{R. Thomas} and \textit{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.
Reviewer (Berlin)
Zbl 0802.05051