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Complexity of Compatible Decompositions of Eulerian Graphs and Their Transformations

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Algorithms — ESA 2002 (ESA 2002)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2461))

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Abstract

In this paper some earlier defined local transformations between eulerian trails are generalized to transformations between decompositions of graphs into (possibly more) closed subtrails. For any graph G with a forbidden partition system F, we give an efficient algorithm which transforms any F-compatible decomposition of G into closed subtrails to another one, and at the same time it preserves F-compatibility and does not increase the number of subtrails by more than one. From this, several earlier results for eulerian trails easily follow. These results are embedded into the rich spectrum of results of theory of eulerian graphs and their applications. We further apply this statement to digraphs and discuss the time complexity of enumeration of all F-compatible decompositions (resp. of all F-compatible eulerian trails) in both graphs and digraphs.

The research was supported by project LN00A056 of the Ministry of Education of the Czech Republic

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Author information

Authors and Affiliations

  1. Department of Applied Mathematics and Institute for Theoretical Computer Science (ITI), Charles University Malostranské nám. 25, 11 800, Praha 1, Czech Republic

    Jana Maxová & Jaroslav Nešetřil

Authors
  1. Jana Maxová
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  2. Jaroslav Nešetřil
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Editor information

Editors and Affiliations

  1. Fakultät II: Mathematik und Naturwissenschaften, Technische Universität Berlin, Strasse des 17. Juni 136, 10623, Berlin, Germany

    Rolf Möhring

  2. Department of Mathematics and Computer Science, University of Leicester, University Road, LE1 7RH, Leicester, UK

    Rajeev Raman

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© 2002 Springer-Verlag Berlin Heidelberg

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Maxová, J., Nešetřil, J. (2002). Complexity of Compatible Decompositions of Eulerian Graphs and Their Transformations. In: Möhring, R., Raman, R. (eds) Algorithms — ESA 2002. ESA 2002. Lecture Notes in Computer Science, vol 2461. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45749-6_62

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  • DOI: https://doi.org/10.1007/3-540-45749-6_62

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-44180-9

  • Online ISBN: 978-3-540-45749-7

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