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Odd Graphs Are Prism-Hamiltonian and Have a Long Cycle

  • Felipe De Campos Mesquita
  • Letícia Rodrigues Bueno
  • Rodrigo De Alencar Hausen
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8392)

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.

Keywords

hamiltonian cycle prism over a graph odd graph 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Felipe De Campos Mesquita
    • 1
  • Letícia Rodrigues Bueno
    • 1
  • Rodrigo De Alencar Hausen
    • 1
  1. 1.Universidade Federal do ABC (UFABC)Santo AndréBrazil

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