Matching Theory (North-Holland mathematics studies)
Matching Theory (North-Holland mathematics studies)
On minimum sets of 1-factors covering a complete multipartite graph
Journal of Graph Theory
On the excessive [m]-index of a tree
Discrete Applied Mathematics
| Hi-index | 0.04 |
An excessive factorization of a multigraph G is a set F={F"1,F"2,...,F"r} of 1-factors of G whose union is E(G) and, subject to this condition, r is minimum. The integer r is called the excessive index of G and denoted by @g"e^'(G). We set @g"e^'(G)=~ if an excessive factorization does not exist. Analogously, let m be a fixed positive integer. An excessive[m]-factorization is a set M={M"1,M"2,...,M"k} of matchings of G, all of size m, whose union is E(G) and, subject to this condition, k is minimum. The integer k is denoted by @g"["m"]^'(G) and called the excessive [m]-index of G. Again, we set @g"["m"]^'(G)=~ if an excessive [m]-factorization does not exist. In this paper we shall prove that, for bipartite multigraphs, both the parameters @g"e^' and @g"["m"]^' are computable in polynomial time, and we shall obtain an efficient algorithm for finding an excessive factorization and excessive [m]-factorization, respectively, of any bipartite multigraph.