Pancomponented 2-factorizations of complete graphs

Dalibor Froncek, Brett Stevens

Research output: Contribution to journalArticle


We pose and solve the existence of 2-factorizations of complete graphs and complete bipartite graphs that have the number of cycles per 2-factor varying, called pancomponented. Such 2-factorizations exist for all such graphs. The pancomponented problem requires a slight generalization of the methods used to solve pancyclic 2-factorization problem, by building 2-factors from cyclically generated 1-factors. These two solutions are offered as the basic approaches to constructing the two essential parameters of a 2-factorization: the size and the number of cycles in the 2-factors.

Original languageEnglish (US)
Pages (from-to)99-112
Number of pages14
JournalDiscrete Mathematics
Issue number1-3
StatePublished - Aug 28 2005


  • 2-Factorization
  • Cycle decomposition
  • Oberwolfach problem

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