Sharply Transitive 1-Factorizations of Complete Multipartite Graphs
نویسندگان
چکیده
Given a finite group G of even order, which graphs Γ have a 1−factorization admitting G as automorphism group with a sharply transitive action on the vertex-set? Starting from this question, we prove some general results and develop an exhaustive analysis when Γ is a complete multipartite graph and G is cyclic.
منابع مشابه
Cyclic and Dihedral 1-Factorizations of Multipartite Graphs
An automorphism group G of a 1-factorization of the complete multipartite graph Km×n consists of permutations of the vertices of the graph mapping factors to factors. In this paper, we give a complete answer to the existence problem of a 1-factorization of Km×n admitting a cyclic or dihedral group acting sharply transitively on the vertices of the graph.
متن کاملOn transitive one-factorizations of arc-transitive graphs
An equivalent relation between transitive 1-factorizations of arctransitive graphs and factorizations of their automorphism groups is established. This relation provides a method for constructing and characterizing transitive 1-factorizations for certain classes of arc-transitive graphs. Then a characterization is given of 2-arc-transitive graphs which have transitive 1factorizations. In this c...
متن کاملVarious One-Factorizations of Complete Graphs
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 ...
متن کاملOn classifying finite edge colored graphs with two transitive automorphism groups
This paper classifies all finite edge colored graphs with doubly transitive automorphism groups. This result generalizes the classification of doubly transitive balanced incomplete block designs with 1 and doubly transitive one-factorizations of complete graphs. It also provides a classification of all doubly transitive symmetric association schemes. The classification of finite simple groups i...
متن کاملHamilton Cycle Rich 2-factorizations of Complete Multipartite Graphs
For any two 2-regular spanning subgraphs G and H of the complete multipartite graph K, necessary and sufficient conditions are found for the existence of a 2-factorization of K in which (1) the first and second 2-factors are isomorphic to G and H respectively, and (2) each other 2-factor is a hamilton cycle, in the case where K has an odd number of vertices.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Electr. J. Comb.
دوره 17 شماره
صفحات -
تاریخ انتشار 2010