Theoretical Computer Science
Monotonicity in graph searching
Journal of Algorithms
Recontamination does not help to search a graph
Journal of the ACM (JACM)
Graph searching and a min-max theorem for tree-width
Journal of Combinatorial Theory Series B
Graph Searching and Interval Completion
SIAM Journal on Discrete Mathematics
Information Processing Letters
Monotonicity of non-deterministic graph searching
Theoretical Computer Science
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Given a simple graph G, we consider the node search problem with inert fugitive. We are interested in minimizing the maximum vertex occupation time, i.e. the maximum number of steps in which a vertex is occupied by a searcher during a search of G. We prove that a search program which does not allow a recontamination may not find an optimal solution to this problem. Moreover, the difference between the minimum maximum vertex occupation time computed by a monotone search program and a program without such a restriction may be arbitrarily large.