Name
Abstract | ||
|---|---|---|
Let i(r, g) denote the infimum of the ratio alpha(G)/vertical bar V(G)vertical bar over the r-regular graphs of girth at least g, where alpha(G) is the independence number of G, and let i(r, infinity) := lim(g ->infinity) i(r, g). Recently, several new lower bounds of i(3, infinity) were obtained. In particular, Hoppen and Wormald showed in 2015 that i(3, infinity) >= 0.4375, and Csoka improved it to i(3, infinity) >= 0.44533 in 2016. Bollobas proved the upper bound i(3, infinity) < 6/13 in 1981, and McKay improved it to i(3, infinity) < 0.45537in 1987. There were no improvements since then. In this paper, we improve the upper bound to i(3, infinity) <= 0.454. |
Year | Venue | Field |
|---|---|---|
2019 | ELECTRONIC JOURNAL OF COMBINATORICS | Discrete mathematics,Combinatorics,Cubic graph,Mathematics |
DocType | Volume | Issue |
Journal | 26 | 1 |
ISSN | Citations | PageRank |
1077-8926 | 0 | 0.34 |
References | Authors | |
0 | 3 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| József Balogh | 1 | 862 | 89.91 |
| Alexandr V. Kostochka | 2 | 682 | 89.87 |
| Xujun Liu | 3 | 0 | 1.69 |