Bert Hartnell - The Watchman's walk problem

Consider the problem of a security firm that is asked to provide protection for a business by monitoring on a regular basis each node of a network. Each point of interest must either be visited or seen from a neighbouring point by a watchman but this need not be on a continuous basis. However, there can be no more than a specified period of time between such monitoring. The security company is to provide the minimum number of watchmen, and to specify the rounds they would have to take, to satisfy this condition. It is not surprising that the general problem does not admit an easy solution, but by imposing suitable restrictions some observations can be made.