Abstract
An excessive factorization of a graph G is a minimum set F of 1-factors of G whose union is E(G). In this paper we study excessive factorizations of regular graphs. We introduce two graph parameters related to excessive factorizations and show that their computation is NP-hard. We pose a number of questions regarding these parameters. We show that the size of an excessive factorization of a regular graph can exceed the degree of the graph by an arbitrarily large quantity. We conclude with a conjecture on the excessive factorizations of r-graphs.
The first author carried out this research within the activity of G.N.S.A.G.A. of the Italian I.N.d.A.M. with the financial support of the Italian Ministry M.I.U.R., project “Strutture geometriche, combinatoria e loro applicazioni.”
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Bonisoli, A., Cariolaro, D. (2006). Excessive Factorizations of Regular Graphs. In: Bondy, A., Fonlupt, J., Fouquet, JL., Fournier, JC., Ramírez Alfonsín, J.L. (eds) Graph Theory in Paris. Trends in Mathematics. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-7400-6_7
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DOI: https://doi.org/10.1007/978-3-7643-7400-6_7
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