Report
A little more about bipartite biregular cages, block designs, and generalized polygons
| العنوان: | A little more about bipartite biregular cages, block designs, and generalized polygons |
|---|---|
| المؤلفون: | Araujo-Pardo, Gabriela, Kiss, György, Szönyi, Tamás |
| سنة النشر: | 2023 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Combinatorics, 05C35, 05C38, 51E05, 51E10, 51E12 |
| الوصف: | In this paper, we obtain new lower and upper bounds for the problem of bipartite biregular cages. Moreover, for girth $6$, we give the exact parameters of the $(m,n;6)$-bipartite biregular cages when $n\equiv -1$ $\pmod m$ using the existence of Steiner System system $S(2,k=m,v=1+n(m-1)+m)$. For girth $g=2r$ and $r=\{4,6,8\}$, we use results on $t$-good structures given by ovoids, spreads and sub-polygons in generalized polygons to obtain $(m,n;2r)$-bipartite biregular graphs. We emphasize that, as we improve the lower bounds on the order of these graphs, we also prove that some of them are $(m,n;2r)$-bipartite biregular cages. In particular, we construct relatively small bipartite biregular graphs from a special class of generalized quadrangles and hexagons. In a special case, we show that the graph obtained is actually a $(3,4;8)$-bipartite biregular cage on $56$ vertices. Comment: 16 pages |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2310.12137 |
| رقم الانضمام: | edsarx.2310.12137 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |