In this paper it is proved that the exponential generating function of the numbers, denoted by N(p, q), of irreducible coverings by edges of the vertices of complete bipartite graphs Kp.q equals exp(xe r + ye x -x -y -xy) -t.
Some properties of irreducible coverings by cliques of complete multipartite graphs
β Scribed by Ioan Tomescu
- Publisher
- Elsevier Science
- Year
- 1980
- Tongue
- English
- Weight
- 923 KB
- Volume
- 28
- Category
- Article
- ISSN
- 0095-8956
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π SIMILAR VOLUMES
A generalization of a recent result of Tomescu ( 1993) is presented. The method is purely combinatorial and is based on the theory of species of several variables.
## Abstract We determine necessary and sufficient conditions for a complete multipartite graph to admit a set of 1βfactors whose union is the whole graph and, when these conditions are satisfied, we determine the minimum size of such a set. Β© 2008 Wiley Periodicals, Inc. J Graph Theory 58:239β250,
## Abstract In this paper we present a simple method for constructing infinite families of graphs defined by a class of systems of equations over commutative rings. We show that the graphs in all such families possess some general properties including regularity and biregularity, existence of speci