Cops & Robber on Periodic Temporal Graphs
Jean-Lou De Carufel, Paola Flocchini, Nicola Santoro, Fr\'ed\'eric, Simard

TL;DR
This paper studies the Cops and Robber game on infinite periodic temporal graphs, providing characterizations, properties, and algorithms for determining copwin conditions for both single and multiple cops.
Contribution
It introduces a unified framework for analyzing Cops and Robber on periodic temporal graphs, extending classical concepts and providing efficient algorithms for copwin determination.
Findings
Characterization of copwin periodic temporal graphs
Efficient algorithm for single cop case
Extension to multiple cops using directed multi-hypergraphs
Abstract
We consider the Cops and Robber pursuit-evasion game when the edge-set of the graph is allowed to change in time, possibly at every round. Specifically, the game is played on an infinite periodic sequence of graphs on the same set of vertices: in round , the topology of is where . Concentrating on the case of a single cop, we provide a characterization of copwin periodic temporal graphs, establishing several basic properties on their nature, and extending to the temporal domain classical C&R concepts such as covers and corners. Based on these results, we design an efficient algorithm for determining if a periodic temporal graph is copwin. We also consider the case of cops. By shifting from a representation in terms of directed graphs to one in terms of directed multi-hypergraphs,…
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Taxonomy
TopicsDNA and Biological Computing · Constraint Satisfaction and Optimization · Data Management and Algorithms
