科研之友
微信
新浪微博
Facebook
分享链接
摘要
We consider upper and lower bounds for gamma (G) + gamma ((G) over bar), the sum of the genus of a graph and its complement. For the lower bound, we show gamma (G) + gamma ((G) over bar) >= inverted right perpendicular1/12 (n(2) - 13n + 24)inverted left perpendicular. Furthermore, we construct an infinite family of graphs attaining this bound along with several other isolated examples. We provide a construction to show that gamma (G) + gamma ((G) over bar) can be at least as large as 1/48 (5n(2) - 52n + 144), and determine sharp upper bounds for a few small orders. Some asymptotic results are considered.
- 出版日期2013-3-28
