Even time constraints on the watchman's walk.
Iain Beaton, Rory Begin, Stephen Finbow, Christopher M. van Bommel · Australas. J Comb. · 2013
In this discrete time process, guards are allowed to traverse edges of a network under the constraint that the neighbourhood of each vertex must be visited within a specified time interval t. Setting t = 0 the guards form a dominating set at all times. We show every rooted tree with relatively few leaves has a branch with a certain order and number of pendant vertices. This result is used to establish the validity of a conjecture of Dyer and Milley regarding the maximum number of guards required when t is even.