منابع مشابه
Excessive near 1-factorizations
We begin the study of sets of near 1-factors of graphs G of odd order whose union contains all the edges of G and determine, for a few classes of graphs, the minimum number of near 1-factors in such sets. MSC 2000: Primary 05C70; Secondary 05C15.
متن کاملExcessive factorizations of bipartite multigraphs
Let G be a multigraph. We say that G is 1-extendable if every edge of G is contained in a 1-factor. Suppose G is 1-extendable. An excessive factorization of G is a set F = {F1, F2, . . . , Fr} 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 χ′e(G). Analogously, let m be a positive integer. We say...
متن کامل1-factorizations of pseudorandom graphs
A 1-factorization of a graph G is a collection of edge-disjoint perfect matchings whose union is E(G). A trivial necessary condition for G to admit a 1-factorization is that |V (G)| is even and G is regular; the converse is easily seen to be false. In this paper, we consider the problem of finding 1-factorizations of regular, pseudorandom graphs. Specifically, we prove that an (n, d, λ)graph G ...
متن کاملOn Semi-perfect 1-Factorizations
The perfect 1-factorization conjecture by A. Kotzig [7] asserts the existence of a 1-factorization of a complete graph K2n in which any two 1-factors induce a Hamiltonian cycle. This conjecture is one of the prominent open problems in graph theory. Apart from its theoretical significance it has a number of applications, particularly in designing topologies for wireless communication. Recently, ...
متن کامل1-Factorizations Of Cayley Graphs
In this note we prove that all connected Cayley graphs of every nite group Q H are 1-factorizable, where Q is any non-trivial group of 2-power order and H is any group of odd order.
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2009
ISSN: 0012-365X
DOI: 10.1016/j.disc.2008.05.035