Hamiltonian cycles in covering graphs of trees

Pavol Hell, Hiroshi Nishiyama, Ladislav Stacho

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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.

Original languageEnglish
Title of host publicationCombinatorial Optimization and Applications - 11th International Conference, COCOA 2017, Proceedings
EditorsXiaofeng Gao, Hongwei Du, Meng Han
PublisherSpringer Verlag
Pages261-275
Number of pages15
ISBN (Print)9783319711461
DOIs
Publication statusPublished - Jan 1 2017
Event11th International Conference on Combinatorial Optimization and Applications, COCOA 2017 - Shanghai, China
Duration: Dec 16 2017Dec 18 2017

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume10628 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference11th International Conference on Combinatorial Optimization and Applications, COCOA 2017
CountryChina
CityShanghai
Period12/16/1712/18/17

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

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    Hell, P., Nishiyama, H., & Stacho, L. (2017). Hamiltonian cycles in covering graphs of trees. In X. Gao, H. Du, & M. Han (Eds.), Combinatorial Optimization and Applications - 11th International Conference, COCOA 2017, Proceedings (pp. 261-275). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 10628 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-319-71147-8_18