Graph embeddings with no Hamiltonian extensions

Abstract

We show that extending an embedding of a graph $\Gamma$ in a surface to an embedding of a Hamiltonian supergraph can be blocked by certain planar subgraphs but, for some subdivisions of $\Gamma$, Hamiltonian extensions must exist.

arXiv comment6 pages, 2 figures; to appear in Bull. of the Inst. of Comb. and its Appl