Minimal k-Connected Non-Hamiltonian Graphs
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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.
KeywordsHamilton cycles Graph minors
- 5.Mark, E., Emily M., Kenta, O., Shoichi, T.: Hamiltonicity of planar graphs with a forbidden minor, Submitted for publication, (October 2016). arXiv:1610.06558