On the number of matchings of a tree

In a paper of Klazar, several counting examples for rooted plane trees were given, including matchings and maximal matchings. Apart from asymptotical analysis, it was shown how to obtain exact formulas for some of the countings by means of the Lagrange inversion formula. In this note, the results of Klazar are extended to formulas for matchings, maximal matchings and maximum matchings for three types of simply generated trees. Finally, edge coverings are considered and the results are compared. Key words. Matchings, maximal matchings, edge coverings, simply generated tree, Lagrange inversion

• Type: Journal
• Year: 2007
• Where: EJC
• Authors: Stephan G. Wagner
• Keywords: EJC 2007, Information Technology, Lagrange Inversion, Lagrange Inversion Formula, Maximal Matchings