Minimal k-Connected Non-Hamiltonian Graphs
In this paper, we explore minimal k-connected non-Hamiltonian graphs. Graphs are said to be minimal in the context of some containment relation; we focus on subgraphs, induced subgraphs, minors, and induced minors. When k= 2 , we discuss all minimal 2-connected non-Hamiltonian graphs for each of these four relations. When k= 3 , we conjecture a set of minimal non-Hamiltonian graphs for the minor relation and we prove one case of this conjecture. In particular, we prove all 3-connected planar triangulations which do not contain the Herschel graph as a minor are Hamiltonian.
Publication Source (Journal or Book title)
Graphs and Combinatorics
Ding, G., & Marshall, E. (2018). Minimal k-Connected Non-Hamiltonian Graphs. Graphs and Combinatorics, 34 (2), 289-312. https://doi.org/10.1007/s00373-018-1874-z