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Hamiltonicity in Split Graphs - A Dichotomy

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Book cover Algorithms and Discrete Applied Mathematics (CALDAM 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10156))

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Abstract

In this paper, we investigate the well-studied Hamiltonian cycle problem, and present an interesting dichotomy result on split graphs. T. Akiyama, T. Nishizeki, and N. Saito [23] have shown that the Hamiltonian cycle problem is NP-complete in planar bipartite graph with maximum degree 3. Using this reduction, we show that the Hamiltonian cycle problem is NP-complete in split graphs. In particular, we show that the problem is NP-complete in \(K_{1,5}\)-free split graphs. Further, we present polynomial-time algorithms for Hamiltonian cycle in \(K_{1,3}\)-free and \(K_{1,4}\)-free split graphs. We believe that the structural results presented in this paper can be used to show similar dichotomy result for Hamiltonian path and other variants of Hamiltonian cycle problem.

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Authors and Affiliations

  1. Indian Institute of Information Technology Design and Manufacturing Kancheepuram, Chennai, India

    P. Renjith & N. Sadagopan

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  1. P. Renjith
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  2. N. Sadagopan
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Correspondence to P. Renjith .

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Editors and Affiliations

  1. University of Lethbridge, Lethbridge, Alberta, Canada

    Daya Gaur

  2. Indian Institute of Technology Madras, Chennai, India

    N.S. Narayanaswamy

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Renjith, P., Sadagopan, N. (2017). Hamiltonicity in Split Graphs - A Dichotomy. In: Gaur, D., Narayanaswamy, N. (eds) Algorithms and Discrete Applied Mathematics. CALDAM 2017. Lecture Notes in Computer Science(), vol 10156. Springer, Cham. https://doi.org/10.1007/978-3-319-53007-9_28

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  • DOI: https://doi.org/10.1007/978-3-319-53007-9_28

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