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What would happen if we have a page of links to other pages likes this.
city 1 blue widget
city 2 blue widget
city 3 blue widget
city 4 blue widget
city 5 blue widget
for the citys we dont offer the service we would like to have free listings for companies that do.
Will we be flagged by the search engines?
The quick test is "are these links of value to my visitors"; id fyes, then proceded - but either use nofollow, or be prepared to check regualrly and frequently for links that 'go bad', else you risk a 'bad beighborhood'.
If the links are for SEO puroposes or a webmaster service, then the best advice is 'forget it' - it's simply not worth the risk. Even if it didn't raise a flag, a rival may dob you in. And if something serious goes wrong with your site, it's one more issue that might have caused it.
I'm not saying that's what you are doing (I cannot know!), but from your description, your sites do sound at risk.
Think about your linking policy, and my "quick test".
Remember that SEs recognise that your outgoing links are your responsibility; you live (or die!) by the consequences of your choices.