Abstract
The odd graph O k is the graph whose vertices are all subsets with k elements of a set {1,…,2k + 1}, and two vertices are joined by an edge if the corresponding pair of k-subsets is disjoint. A conjecture due to Biggs claims that O k is hamiltonian for k ≥ 3 and a conjecture due to Lovász implies that O k has a hamiltonian path for k ≥ 1. In this paper, we show that the prism over O k is hamiltonian and that O k has a cycle with .625|V(O k )| vertices at least.
Research partially supported by Brazilian agency CNPq.
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De Campos Mesquita, F., Bueno, L.R., De Alencar Hausen, R. (2014). Odd Graphs Are Prism-Hamiltonian and Have a Long Cycle. In: Pardo, A., Viola, A. (eds) LATIN 2014: Theoretical Informatics. LATIN 2014. Lecture Notes in Computer Science, vol 8392. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-54423-1_33
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DOI: https://doi.org/10.1007/978-3-642-54423-1_33
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