Are highly connected 1-planar graphs Hamiltonian? [article]

Therese Biedl
2019 arXiv   pre-print
It is well-known that every planar 4-connected graph has a Hamiltonian cycle. In this paper, we study the question whether every 1-planar 4-connected graph has a Hamiltonian cycle. We show that this is false in general, even for 5-connected graphs, but true if the graph has a 1-planar drawing where every region is a triangle.
arXiv:1911.02153v1 fatcat:v2w2mtwuvbe5xhamignpmimwkm