Opening book details…
Can I read An Existence Theory for Loopy Graph Decompositions on EtoBox?
An Existence Theory for Loopy Graph Decompositions by Peter Dukes; Amanda Malloch is a Engineering article available to read on EtoBox.
What is An Existence Theory for Loopy Graph Decompositions about?
Let v ≥ k ≥ 1 and k ≥ 0 be integers. Recall that a (v, k, k) block design is a collection B of k-subsets of a v-set X in which every unordered pair of elements in X is contained in exactly k of the subsets in B. Now let G be a graph with no multiple edges. A (v, G, k) graph design is a collection H of subgraphs, each isomoprhic to G, of the complete graph K v such that each edge of K v appears in exactly k of the subgraphs in H. A famous result of Wilson states that for a fixed simple graph G and integer k, there exists a (v, G, k) graph design for all sufficiently large integers v satisfying certain necessary conditions. Here, we extend this result to include the case of loops in G. As a consequence, we obtain the asymptotic existence of equireplicate graph designs. Applications of the equireplicate condition are given.
Who reads An Existence Theory for Loopy Graph Decompositions?
It is typically read by researchers, students, and practitioners in Engineering.
- Author
- Peter Dukes; Amanda Malloch
- Publisher
- John Wiley and Sons; Wiley (John Wiley & Sons); John Wiley & Sons Inc.; Wiley (ISSN 1063-8539)
- Published
- 2011
- Language
- EN
- Field
- Engineering (Physical Sciences)