Odd Graphs Are Prism-Hamiltonian and Have a Long Cycle
نویسندگان
چکیده
The odd graph Ok has the subsets with k elements of a set {1, . . . , 2k + 1} as its vertices set, and there exists an edge between two vertices if the corresponding pair of k-subsets is disjoint. A conjecture claims that Ok is hamiltonian for k > 2 and another long-standing conjecture implies that all odd graphs have a hamiltonian path. We proved that the prism over Ok is hamiltonian and that Ok has a cycle with at least .625|V (Ok)| vertices.
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