Covering graphs with matchings of fixed size

David Cariolaro*, Hung-Lin Fu

*Corresponding author for this work

Research output: Contribution to journalArticle

6 Scopus citations

Abstract

Let m be a positive integer and let G be a graph. We consider the question: can the edge set E (G) of G be expressed as the union of a set M of matchings of G each of which has size exactly m? If this happens, we say that G is [m]-coverable and we call M an [m]-covering of G. It is interesting to consider minimum[m] -coverings, i.e. [m]-coverings containing as few matchings as possible. Such [m]-coverings will be called excessive[m] -factorizations. The number of matchings in an excessive [m]-factorization is a graph parameter which will be called the excessive[m] -index and denoted by χ[m]. In this paper we begin the study of this new parameter as well as of a number of other related graph parameters.

Original languageEnglish
Pages (from-to)276-287
Number of pages12
JournalDiscrete Mathematics
Volume310
Issue number2
DOIs
StatePublished - 28 Jan 2010

Keywords

  • Excessive [m]-factorization
  • Excessive [m]-index
  • [m]-covering

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