The asymptotic existence of graph decompositions with loops
| dc.contributor.author | Malloch, Amanda | |
| dc.contributor.supervisor | Dukes, Peter | |
| dc.date.accessioned | 2009-08-31T21:34:58Z | |
| dc.date.available | 2009-08-31T21:34:58Z | |
| dc.date.copyright | 2009 | en |
| dc.date.issued | 2009-08-31T21:34:58Z | |
| dc.degree.department | Department of Mathematics and Statistics | |
| dc.degree.level | Master of Science M.Sc. | en |
| dc.description.abstract | Let v [greater than or equal to] k [greater than or equal to] 1 and lamda [greater than or equal to] 0 be integers and G be a graph with n vertices, m edges, and no multiple edges. A (v, k, lambda) block design is a collection Beta of k-subsets of a v-set X in which every unordered pair of elements in X is contained in exactly lambda of the subsets in Beta. A (G-decomposition, or (v, G, lambda) graph design, is a collection H1, H2, ..., Ht of subgraphs of Kv (the complete graph on v vertices) such that each edge of Kv is an edge of exactly lambda of the subgraphs Hi and each of the subgraphs Hi is isomorphic to G. A famous result by Wilson says that for a fixed graph G and integer lambda, there exists a (v, G, lambda) graph design for all sufficiently large integers v satisfying certain necessary conditions. In this thesis, we extend this result to include the case of loops in G. As a consequence, one obtains asymptotic existence of equireplicate graph designs for values of v satisfying certain necessary conditions, where a graph design is called equireplicate if each vertex of Kv occurs in the same number of subgraphs Hi of the decomposition. | en |
| dc.identifier.uri | http://hdl.handle.net/1828/1705 | |
| dc.language | English | eng |
| dc.language.iso | en | en |
| dc.rights | Available to the World Wide Web | en |
| dc.subject | graph decomposition | en |
| dc.subject | design theory | en |
| dc.subject.lcsh | UVic Subject Index::Sciences and Engineering | en |
| dc.title | The asymptotic existence of graph decompositions with loops | en |
| dc.type | Thesis | en |