Name
Abstract | ||
|---|---|---|
We determine that there is no partial geometry G with parameters (s,t,α)=(4,27,2). The existence of such a geometry has been a challenging open problem of interest to researchers for almost 40 years. The particular interest in G is due to the fact that it would have the exceptional McLaughlin graph as its point graph. Our proof makes extensive use of symmetry and high-performance distributed computing, and details of our techniques and checks are provided. One outcome of our work is to show that a pseudogeometric strongly regular graph achieving equality in the Krein bound need not be the point graph of any partial geometry. |
Year | DOI | Venue |
|---|---|---|
2018 | 10.1016/j.jcta.2017.10.004 | Journal of Combinatorial Theory, Series A |
Keywords | Field | DocType |
Partial geometry,Pseudogeometric graph,McLaughlin geometry,McLaughlin graph,Krein bound,Backtrack search | Partial geometry,Discrete mathematics,Graph,Combinatorics,Strongly regular graph,Open problem,Geometry,Mathematics | Journal |
Volume | ISSN | Citations |
155 | 0097-3165 | 0 |
PageRank | References | Authors |
0.34 | 0 | 2 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Patric R. J. Östergård | 1 | 609 | 70.61 |
| Leonard H. Soicher | 2 | 48 | 10.38 |