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Hamiltonian Cycles in Covering Graphs of Trees

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Combinatorial Optimization and Applications (COCOA 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10628))

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Abstract

Hamiltonicity of graphs possessing symmetry has been a popular subject of research, with focus on vertex-transitive graphs, and in particular on Cayley graphs. In this paper, we consider the Hamiltonicity of another class of graphs with symmetry, namely covering graphs of trees. In particular, we study the problem for covering graphs of trees, where the tree is a voltage graph over a cyclic group. Batagelj and Pisanski were first to obtain such a result, in the special case when the voltage assignment is trivial; in that case, the covering graph is simply a Cartesian product of the tree and a cycle. We consider more complex voltage assignments, and extend the results of Batagelj and Pisanski in two different ways; in these cases the covering graphs cannot be expressed as products. We also provide a linear time algorithm to test whether a given assignment satisfies these conditions.

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Notes

  1. 1.

    Two paths P and Q are internally vertex disjoint if there is no vertex that is an internal vertex of P and is an internal vertex of Q.

  2. 2.

    A branching vertex is a vertex of degree at least three.

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Author information

Authors and Affiliations

  1. School of Computing Science, Simon Fraser University, Burnaby, BC, V5A 1S6, Canada

    Pavol Hell

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

    Hiroshi Nishiyama

  3. Department of Mathematics, Simon Fraser University, Burnaby, BC, V5A 1S6, Canada

    Ladislav Stacho

Authors
  1. Pavol Hell
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  2. Hiroshi Nishiyama
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  3. Ladislav Stacho
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Corresponding author

Correspondence to Hiroshi Nishiyama .

Editor information

Editors and Affiliations

  1. Shanghai Jiao Tong University, Shanghai, China

    Xiaofeng Gao

  2. Harbin Institute of Technology, Shenzhen, China

    Hongwei Du

  3. Kennesaw State University, Kennesaw, Georgia, USA

    Meng Han

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Hell, P., Nishiyama, H., Stacho, L. (2017). Hamiltonian Cycles in Covering Graphs of Trees. In: Gao, X., Du, H., Han, M. (eds) Combinatorial Optimization and Applications. COCOA 2017. Lecture Notes in Computer Science(), vol 10628. Springer, Cham. https://doi.org/10.1007/978-3-319-71147-8_18

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  • DOI: https://doi.org/10.1007/978-3-319-71147-8_18

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-71146-1

  • Online ISBN: 978-3-319-71147-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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