Even time constraints on the watchman's walk
نویسندگان
چکیده
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.
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ورودعنوان ژورنال:
- Australasian J. Combinatorics
دوره 56 شماره
صفحات -
تاریخ انتشار 2013