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The Parity Hamiltonian Cycle Problem in Directed Graphs

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Book cover Combinatorial Optimization (ISCO 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9849))

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Abstract

This paper investigates a variant of the Hamiltonian cycle, the parity Hamiltonian cycle (PHC) problem: a PHC in a directed graph is a closed walk (possibly using an arc more than once) which visits every vertex odd number of times. Nishiyama et al. (2015) investigated the undirected version of the PHC problem, and gave a simple characterization that a connected undirected graph has a PHC if and only if it has even order or it is non-bipartite. This paper gives a complete characterization when a directed graph has a PHC, and shows that the PHC problem in a directed graph is solved in polynomial time. The characterization, unlike with the undirected case, is described by a linear system over GF(2).

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Acknowledgements

This work is partly supported by JSPS KAKENHI Grant Number 15K15938, 25700002, 15H02666, and Grant-in-Aid for Scientific Research on Innovative Areas MEXT Japan “Exploring the Limits of Computation (ELC).”

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Authors and Affiliations

  1. Graduate School of Information Science and Electrical Engineering, Kyushu University, Fukuoka, Japan

    Hiroshi Nishiyama, Yukiko Yamauchi, Shuji Kijima & Masafumi Yamashita

Authors
  1. Hiroshi Nishiyama
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  2. Yukiko Yamauchi
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  3. Shuji Kijima
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  4. Masafumi Yamashita
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Corresponding author

Correspondence to Hiroshi Nishiyama .

Editor information

Editors and Affiliations

  1. University of Salerno , Fisciano, Italy

    Raffaele Cerulli

  2. Kyoto University , Kyoto, Japan

    Satoru Fujishige

  3. LAMSADE, Université Paris-Dauphine , Paris , France

    A. Ridha Mahjoub

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Nishiyama, H., Yamauchi, Y., Kijima, S., Yamashita, M. (2016). The Parity Hamiltonian Cycle Problem in Directed Graphs. In: Cerulli, R., Fujishige, S., Mahjoub, A. (eds) Combinatorial Optimization. ISCO 2016. Lecture Notes in Computer Science(), vol 9849. Springer, Cham. https://doi.org/10.1007/978-3-319-45587-7_5

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  • DOI: https://doi.org/10.1007/978-3-319-45587-7_5

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-45586-0

  • Online ISBN: 978-3-319-45587-7

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