On one-factorizations of the complete graph
نویسندگان
چکیده
منابع مشابه
Sequentially Perfect and Uniform One-Factorizations of the Complete Graph
In this paper, we consider a weakening of the definitions of uniform and perfect one-factorizations of the complete graph. Basically, we want to order the 2n − 1 one-factors of a one-factorization of the complete graph K2n in such a way that the union of any two (cyclically) consecutive one-factors is always isomorphic to the same two-regular graph. This property is termed sequentially uniform;...
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LetF be a 2-factorization of the complete graphKv admitting an automorphism groupG acting primitively on the set of vertices. IfF consists of Hamiltonian cycles, thenF is the unique, up to isomorphisms, 2-factorization ofKpn admitting an automorphism group which acts 2-transitively on the vertex-set, see [A. Bonisoli, M. Buratti, G. Mazzuoccolo, Doubly transitive 2-factorizations, J. Combin.Des...
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We introduce the concept of a 2-starter in a groupG of odd order.We prove that any 2-factorization of the complete graph admitting G as a sharply vertex transitive automorphism group is equivalent to a suitable 2-starter in G. Some classes of 2-starters are studied, with special attention given to those leading to solutions of some Oberwolfach or Hamilton–Waterloo problems. © 2005 Elsevier Inc....
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Methods to compute 1–factorizations of a complete graphs of even order are presented. For complete graphs where the number of vertices is a power of 2, we propose several new methods to construct 1–factorizations. Our methods are different from methods that make use of algebraic concepts such as Steiner triple systems, starters and all other existing methods. We also show that certain complete ...
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Consider factorizations into transpositions of an n-cycle in the symmetric group Sn. To every such factorization we assign a monomial in variables wij that retains the transpositions used, but forgets their order. Summing over all possible factorizations of n-cycles we obtain a polynomial that happens to admit a closed expression. From this expression we deduce a formula for the number of 1-fac...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1987
ISSN: 0012-365X
DOI: 10.1016/0012-365x(87)90030-6