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A constrained path decomposition of cubic graphs and the path number of cacti

  • Fábio Botler
  • Yoshiko Wakabayashi
Conference paper
Part of the CRM Series book series (PSNS, volume 16)

Abstract

Kotzig (1957) proved that a cubic graph has a perfect matching if and only if it has a 3-path decomposition (that is, a partition of the edge set into paths of length 3). This result was generalized by Jaeger, Payan, and Kouider (1983), who proved that a (2k + l)-regular graph with a perfect matching can be decomposed into bistars. (A bistar is a graph obtained from two disjoint stars by joining their centers with an edge.) In another direction, Heinrich, Liu and Yu (1999) proved that a 3m-regular graph G admits a balanced 3-path decomposition if and only if G contains an m-factor.

Copyright information

© Scuola Normale Superiore Pisa 2013

Authors and Affiliations

  • Fábio Botler
    • 1
  • Yoshiko Wakabayashi
    • 1
  1. 1.Institute of Mathematics and StatisticsUniversity of São PauloBrazil

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