Every 4-Connected Graph with Crossing Number 2 is Hamiltonian
Kenta Ozeki, Carol T. Zamfirescu · SIAM Journal on Discrete Mathematics · 2018
A seminal theorem of Tutte states that 4-connected planar graphs are Hamiltonian. Applying a result of Thomas and Yu, 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.