## Infinitely many planar cubic hypohamiltonian graphs of girth 5.(English)Zbl 1391.05153

Summary: A graph $$G$$ is hypohamiltonian if $$G$$ is non-Hamiltonian and for every vertex $$v$$ in $$G$$, the graph $$G-v$$ is Hamiltonian. B. D. McKay [J. Graph Theory 85, No. 1, 7–11 (2017; Zbl 1365.05064)] asked whether infinitely many planar cubic hypohamiltonian graphs of girth 5 exist. We settle this question affirmatively.

### MSC:

 05C45 Eulerian and Hamiltonian graphs 05C10 Planar graphs; geometric and topological aspects of graph theory

### Keywords:

cubic; dot product; Hamiltonian graph; hypo-Hamiltonian graph

Zbl 1365.05064
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