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2017 | OriginalPaper | Buchkapitel

Hamiltonian Cycles in Covering Graphs of Trees

verfasst von : Pavol Hell, Hiroshi Nishiyama, Ladislav Stacho

Erschienen in: Combinatorial Optimization and Applications

Verlag: Springer International Publishing

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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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Fußnoten
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
A branching vertex is a vertex of degree at least three.
 
Literatur
2.
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Zurück zum Zitat Curran, S.J., Gallian, J.A.: Hamiltonian cycles and paths in Cayley graphs and digraphs - a survey. Discrete Math. 156, 1–18 (1996)CrossRefMATHMathSciNet Curran, S.J., Gallian, J.A.: Hamiltonian cycles and paths in Cayley graphs and digraphs - a survey. Discrete Math. 156, 1–18 (1996)CrossRefMATHMathSciNet
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Zurück zum Zitat Kutner, K., Marušič, R.: Hamilton cycles and paths in vertex-transitive graphs - current directions. Discrete Math. 309, 5491–5500 (2009)CrossRefMATHMathSciNet Kutner, K., Marušič, R.: Hamilton cycles and paths in vertex-transitive graphs - current directions. Discrete Math. 309, 5491–5500 (2009)CrossRefMATHMathSciNet
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Zurück zum Zitat Lakshmivarahan, S., Jwo, J.-S., Dhall, S.K.: Symmetry in interconnection networks based on Cayley graphs of permutation groups: a survey. Parallel Comput. 19, 361–407 (1993)CrossRefMATHMathSciNet Lakshmivarahan, S., Jwo, J.-S., Dhall, S.K.: Symmetry in interconnection networks based on Cayley graphs of permutation groups: a survey. Parallel Comput. 19, 361–407 (1993)CrossRefMATHMathSciNet
8.
Zurück zum Zitat Pisanski, T., Žerovnik, J.: Hamilton cycles in graph bundles over a cycle with tree as a fibre. Discrete Math. 309, 5432–5436 (2009)CrossRefMATHMathSciNet Pisanski, T., Žerovnik, J.: Hamilton cycles in graph bundles over a cycle with tree as a fibre. Discrete Math. 309, 5432–5436 (2009)CrossRefMATHMathSciNet
Metadaten
Titel
Hamiltonian Cycles in Covering Graphs of Trees
verfasst von
Pavol Hell
Hiroshi Nishiyama
Ladislav Stacho
Copyright-Jahr
2017
DOI
https://doi.org/10.1007/978-3-319-71147-8_18