The complexity of searching a graph
Journal of the ACM (JACM)
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
The vertex separation and search number of a graph
Information and Computation
Capture of an intruder by mobile agents
Proceedings of the fourteenth annual ACM symposium on Parallel algorithms and architectures
Sweeping graphs with large clique number
ISAAC'04 Proceedings of the 15th international conference on Algorithms and Computation
Connected treewidth and connected graph searching
LATIN'06 Proceedings of the 7th Latin American conference on Theoretical Informatics
An annotated bibliography on guaranteed graph searching
Theoretical Computer Science
Monotonicity of non-deterministic graph searching
Theoretical Computer Science
Monotony properties of connected visible graph searching
Information and Computation
Monotonicity of non-deterministic graph searching
WG'07 Proceedings of the 33rd international conference on Graph-theoretic concepts in computer science
The cost of monotonicity in distributed graph searching
OPODIS'07 Proceedings of the 11th international conference on Principles of distributed systems
A fast robot path planning algorithm based on image thinning
ICIRA'10 Proceedings of the Third international conference on Intelligent robotics and applications - Volume Part I
Distributed security algorithms by mobile agents
ICDCN'06 Proceedings of the 8th international conference on Distributed Computing and Networking
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Search games are attractive for their correspondence with classical width parameters. For instance, the invisible search number (a.k.a. node search number) of a graph is equal to its pathwidth plus 1, and the visible search number of a graph is equal to its treewidth plus 1. The connected variants of these games ask for search strategies that are connected, i.e., at every step of the strategy, the searched part of the graph induces a connected subgraph. We focus on monotone search strategies, i.e., strategies for which every node is searched exactly once. It is known that the monotone connected visible search number of an n-node graph is at most O(logn) times its visible search number. First, we prove that this logarithmic bound is tight. Precisely, we prove that there is an infinite family of graphs for which the ratio monotone connected visible search number over visible search number is Ω(logn). Second, we prove that, as opposed to the non-connected variant of visible graph searching, “recontamination helps” for connected visible search. Precisely, we describe an infinite family of graphs for which any monotone connected visible search strategy for any graph in this family requires strictly more searchers than the connected visible search number of the graph.