The article discusses the generation of K2-hypohamiltonian graphs, introducing new families through operations preserving K2-hypohamiltonicity and planarity. It presents an algorithm to generate all pairwise non-isomorphic K2-hypohamiltonian graphs and explores the existence of bipartite K2-hypohamiltonian graphs. The results include characterizing the orders for which planar K2-hypohamiltonian graphs exist and determining the minimum order for various types of K2-hypohamiltonian graphs.
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arxiv.org
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