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Decomposing Semi-complete Multigraphs and Directed Graphs into Paths of Length Two

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Algorithms and Discrete Applied Mathematics (CALDAM 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10156))

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Abstract

A \(P_3\)-decomposition of a graph is a partition of the edges of the graph into paths of length two. We give a simple necessary and sufficient condition for a semi-complete multigraph, that is a multigraph with at least one edge between each pair of vertices, to have a \(P_3\)-decomposition. We show that this condition can be tested in strongly polynomial-time, and that the same condition applies to a larger class of multigraphs. We give a similar condition for a \(P_3\)-decomposition of a semi-complete directed graph. In particular, we show that a tournament admits a \(P_3\)-decomposition iff its outdegree sequence is the degree sequence of a simple undirected graph.

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Authors and Affiliations

  1. Department of Computer Science and Engineering, Indian Institute of Technology Bombay, Powai, Mumbai, 400076, India

    Ajit A. Diwan & Sai Sandeep

Authors
  1. Ajit A. Diwan
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  2. Sai Sandeep
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Correspondence to Ajit A. Diwan .

Editor information

Editors and Affiliations

  1. University of Lethbridge, Lethbridge, Alberta, Canada

    Daya Gaur

  2. Indian Institute of Technology Madras, Chennai, India

    N.S. Narayanaswamy

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Diwan, A.A., Sandeep, S. (2017). Decomposing Semi-complete Multigraphs and Directed Graphs into Paths of Length Two. In: Gaur, D., Narayanaswamy, N. (eds) Algorithms and Discrete Applied Mathematics. CALDAM 2017. Lecture Notes in Computer Science(), vol 10156. Springer, Cham. https://doi.org/10.1007/978-3-319-53007-9_15

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  • DOI: https://doi.org/10.1007/978-3-319-53007-9_15

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-53006-2

  • Online ISBN: 978-3-319-53007-9

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