Monotonicity in graph searching
Journal of Algorithms
Graph searching and a min-max theorem for tree-width
Journal of Combinatorial Theory Series B
Minimal acyclic forbidden minors for the family of graphs with bounded path-width
Discrete Mathematics - Special issue on graph theory and applications
The vertex separation and search number of a graph
Information and Computation
Mixed searching and proper-path-width
Theoretical Computer Science
Multiplicities of eigenvalues and tree-width of graphs
Journal of Combinatorial Theory Series B
Algorithms and obstructions for linear-width and related search parameters
Discrete Applied Mathematics
Digraph measures: Kelly decompositions, games, and orderings
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Nondeterministic graph searching: from pathwidth to treewidth
MFCS'05 Proceedings of the 30th international conference on Mathematical Foundations of Computer Science
An annotated bibliography on guaranteed graph searching
Theoretical Computer Science
Searching for a Visible, Lazy Fugitive
Graph-Theoretic Concepts in Computer Science
| Hi-index | 0.00 |
We define helicopter cop and robber games with multiple robbers, extending previous research, which only considered the pursuit of a single robber. Our model is defined for robbers that are visible (the cops know their position) and active (able to move at every turn) but is easily adapted to other common variants of the game. The game with many robbers is non-monotone: more cops are needed if their moves are restricted so as to monotonically decrease the space available to the robbers. Because the cops may decide their moves based on the robbers' current position, strategies in the game are interactive but the game becomes, in a sense, less interactive as the initial number of robbers increases. We prove that the main parameter emerging from the game captures a hierarchy of parameters between proper pathwidth and proper treewidth. We give a complete characterization of the parameter for trees and an upper bound for general graphs.