5 papers
Minors of non-hamiltonian polyhedra and the Herschel family
On-Hei Solomon Lo, Kenta Ozeki
We show that every non-hamiltonian polyhedron contains the Herschel graph as a minor, implying that the Herschel graph is the unique minor-minimal non-hamiltonian polyhedron. Our a…
A note on cycles in cyclically -edge-connected cubic planar graphs
On-Hei Solomon Lo
Let be obtained from a cyclically -edge-connected cubic planar graph other than by deleting two adjacent vertices. We provide a short proof that if has circumf…
A characterization of graphs with no minor
On-Hei Solomon Lo
A complete structural characterization of graphs with no minor is obtained, and the following consequences are established. Every -connected non-planar graph with at l…
On minors of non-hamiltonian graphs
On-Hei Solomon Lo
A theorem of Tutte states that every 4-connected non-hamiltonian graph contains as a minor. We strengthen this result by proving that such a graph must contain …
Colouring normal quadrangulations of projective spaces
Tomáš Kaiser, On-Hei Solomon Lo, Atsuhiro Nakamoto +2
Youngs proved that every non-bipartite quadrangulation of the projective plane is 4-chromatic. Kaiser and Stehl\'ık [J. Combin. Theory Ser. B 113 (2015),…