Theoretical Computer Science
The complexity of searching a graph
Journal of the ACM (JACM)
Nonconstructive tools for proving polynomial-time decidability
Journal of the ACM (JACM)
Monotonicity in graph searching
Journal of Algorithms
Graph minors: X. obstructions to tree-decomposition
Journal of Combinatorial Theory Series B
Recontamination does not help to search a graph
Journal of the ACM (JACM)
Approximating treewidth, pathwidth, frontsize, and shortest elimination tree
Journal of Algorithms
Minimal acyclic forbidden minors for the family of graphs with bounded path-width
Discrete Mathematics - Special issue on graph theory and applications
Graph minors. XIII: the disjoint paths problem
Journal of Combinatorial Theory Series B
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Eavesdropping games: a graph-theoretic approach to privacy in distributed systems
Journal of the ACM (JACM)
An agent-based approach for building complex software systems
Communications of the ACM
Capture of an intruder by mobile agents
Proceedings of the fourteenth annual ACM symposium on Parallel algorithms and architectures
On the monotonicity of games generated by symmetric submodular functions
Discrete Applied Mathematics - Submodularity
Graph Minors. XX. Wagner's conjecture
Journal of Combinatorial Theory Series B - Special issue dedicated to professor W. T. Tutte
Large Mesh Simplification using Processing Sequences
Proceedings of the 14th IEEE Visualization 2003 (VIS'03)
Distributed chasing of network intruders
Theoretical Computer Science
An annotated bibliography on guaranteed graph searching
Theoretical Computer Science
Decontamination of hypercubes by mobile agents
Networks - Games, Interdiction, and Human Interaction Problems on Networks
Monotony properties of connected visible graph searching
Information and Computation
Theoretical Computer Science
Connected graph searching in chordal graphs
Discrete Applied Mathematics
Generalized hypertree decompositions: NP-hardness and tractable variants
Journal of the ACM (JACM)
Pathwidth is NP-Hard for Weighted Trees
FAW '09 Proceedings of the 3d International Workshop on Frontiers in Algorithmics
Connected searching of weighted trees
Theoretical Computer Science
Connected treewidth and connected graph searching
LATIN'06 Proceedings of the 7th Latin American conference on Theoretical Informatics
Approximate search strategies for weighted trees
Theoretical Computer Science
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In the graph searching game the opponents are a set of searchers and a fugitive in a graph. The searchers try to capture the fugitive by applying some sequence of moves that include placement, removal, or sliding of a searcher along an edge. The fugitive tries to avoid capture by moving along unguarded paths. The search number of a graph is the minimum number of searchers required to guarantee the capture of the fugitive. In this paper, we initiate the study of this game under the natural restriction of connectivity where we demand that in each step of the search the locations of the graph that are clean (i.e. non-accessible to the fugitive) remain connected. We give evidence that many of the standard mathematical tools used so far in classic graph searching fail under the connectivity requirement. We also settle the question on ''the price of connectivity'', that is, how many searchers more are required for searching a graph when the connectivity demand is imposed. We make estimations of the price of connectivity on general graphs and we provide tight bounds for the case of trees. In particular, for an n-vertex graph the ratio between the connected searching number and the non-connected one is O(logn) while for trees this ratio is always at most 2. We also conjecture that this constant-ratio upper bound for trees holds also for all graphs. Our combinatorial results imply a complete characterization of connected graph searching on trees. It is based on a forbidden-graph characterization of the connected search number. We prove that the connected search game is monotone for trees, i.e. restricting search strategies to only those where the clean territories increase monotonically does not require more searchers. A consequence of our results is that the connected search number can be computed in polynomial time on trees, moreover, we show how to make this algorithm distributed. Finally, we reveal connections of this parameter to other invariants on trees such as the Horton-Strahler number.