# Minimal k-Connected Non-Hamiltonian Graphs

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\$\$ 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Graphs and Combinatorics Springer Journals

# Minimal k-Connected Non-Hamiltonian Graphs

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### Abstract

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.

### Journal

Graphs and CombinatoricsSpringer Journals

Published: Feb 14, 2018

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