Hoa's Conjecture on Maximal Non-Hamiltonian Graphs
Statement
A graph is maximal non-Hamiltonian if it is non-Hamiltonian but is Hamiltonian for every nonedge . In 1994 Vu Dinh Hoa conjectured a property of for a longest cycle of such a graph. Disproved by an explicit base graph on 56 vertices, extended to larger orders.
Context
A named 1994 conjecture in Hamiltonian graph theory with a small but real literature; the audience is specialists in cycle structure.
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