Symmetric Bowtie Decompositions of the Complete Graph

Symmetric Bowtie Decompositions of the Complete Graph

Given a bowtie decomposition of the complete graph Kv admitting an automorphism group G acting transitively on the vertices of the graph, we give necessary conditions involving the rank of the group and the cycle types of the permutations in G. These conditions yield non–existence results for instance when G is the dihedral group of order 2v, with v ≡ 1, 9 (mod 12), or a group acting transitive...

Cycle decompositions of the complete graph

For a positive integer n, let G be Kn if n is odd and Kn less a one-factor if n is even. In this paper it is shown that, for non-negative integers p, q and r, there is a decomposition of G into p 4-cycles, q 6-cycles and r 8-cycles if 4p+6q+8r = |E(G)|, q = 0 if n < 6 and r = 0 if n < 8.

Symmetric Hamilton cycle decompositions of complete multigraphs

Let n ≥ 3 and λ ≥ 1 be integers. Let λKn denote the complete multigraph with edge-multiplicity λ. In this paper, we show that there exists a symmetric Hamilton cycle decomposition of λK2m for all even λ ≥ 2 and m ≥ 2. Also we show that there exists a symmetric Hamilton cycle decomposition of λK2m − F for all odd λ ≥ 3 and m ≥ 2. In fact, our results together with the earlier results (by Walecki...

Lambda-fold complete graph decompositions into perfect four-triple configurations

Hamilton surfaces for the complete even symmetric bipartite graph

A cycle in a graph G is called a hamilton cycle if it contains every vertex of G. A l-factor of a graph G is a subgraph H of G with the same vertex set as G, such that each vertex of H has degree one. Ringel [S] has generalized the idea of a hamilton cycle to two dimensions. He showed that if n is odd the set of squares in the n-dimensional cube Q,, can be partitioned into subsets such that eac...