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 $$k=2$$ k = 2 , we discuss all minimal 2-connected non-Hamiltonian graphs for each of these four relations. When $$k=3$$ 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.
Graphs and Combinatorics – Springer Journals
Published: Feb 14, 2018
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