And Food Lion, Hannaford, Peapod and Bfresh.
In Europe also Albert Heijn (mostly NL, which is where the 'ah' in ahold comes from, it stands for Albert Heijn Holding) and Delhaize (Belgium, France and lots of countries in Eastern Europe with various brands such as Mega Image, Shop and Go, AB * and tons of other brands besides).
They're huge and because of the vast number of brands it is quite hard to get a grip on just how large they are.
In 2012, this article puts grocery revenue at $255b (over twice krogers revenue): http://money.cnn.com/2013/01/31/news/companies/walmart-groce...
And this article says they have 25% of the 700b grocery market: http://www.salon.com/2013/03/28/will_wal_mart_replace_the_su...
And this article says "Wal-Mart's biggest revenue driver is food (55%)".. and walmart has 485b in total revenue: https://www.fool.com/investing/general/2014/07/16/kroger-wal...
Different sources give different rankings, often very different. I picked that one because it was the only one I found at the time that put Whole Foods at #6, so at least might be the ordering the article author was thinking of.
It's also not clear how largeness should be measured. Some lists seem to be by sales. Some seem to be by number of stores. Some seem to be by number of employees. It's not always clear which a given list is using.
For the curios, the five bigger seem to be, in descending order: Kroger, Albertsons, Ahold USA, Publix, and H-E-B Grocery. (Walmart is #7).
Ahold owns Giant, Martin's, Stop & Shop.