Catching a Fast Robber on Interval Graphs

  title={Catching a Fast Robber on Interval Graphs},
  author={Tom{\'a}{\vs} Gaven{\vc}iak},
We analyse the Cops and ∞-fast Robber game on the class of interval graphs and show it to be polynomially decidable on such graphs. This solves an open problem posed in paper "Pursuing a fast robber on a graph" by Fomin et al. [4] The game is known to be already NP-hard on chordal graphs and split-graphs. The game is played by two players, one controlling k cops, the other a robber. The players alternate in turns, all the cops move at once to distance at most one, the robber moves along any… 
The fast robber on interval and chordal graphs
Chasing a Fast Robber on Planar Graphs and Random Graphs
We consider a variant of the Cops and Robber game, in which the robber has unbounded speed, that is, can take any path from her vertex in her turn, but she is not allowed to pass through a vertex
Algorithmic complexity: Between Structure and Knowledge How Pursuit-evasion Games help. (Complexité algorithmique: entre structure et connaissance. Comment les jeux de poursuite peuvent apporter des solutions)
This manuscript describes the work of the author since he obtained his Ph.D. in 2007, which deals with new algorithmic challenges posed by the growth of nowadays networks and by the increased data and traffi c arising in it.


On tractability of Cops and Robbers game
It is proved that computing the minimum number of cops that can catch a robber on a given graph is NP-hard, and it is shown that the parameterized version of the problem is W[2]-hard.
Pursuing a fast robber on a graph
Vertex-to-vertex pursuit in a graph
An Incremental Linear-Time Algorithm for Recognizing Interval Graphs
This paper presents a much simpler algorithm using a related, but much more informative tree representation of interval graphs.
Modern Graph Theory
This book presents an account of newer topics, including Szemer'edi's Regularity Lemma and its use; Shelah's extension of the Hales-Jewett Theorem; the precise nature of the phase transition in a random graph process; the connection between electrical networks and random walks on graphs; and the Tutte polynomial and its cousins in knot theory.
Lessons in Play: An Introduction to Combinatorial Game Theory
Classic techniques are introduced and applied in novel ways to analyze both old and new games, several appearing for the first time in this book.
Graduate Texts in Mathematics
Graduate Texts in Mathematics bridge the gap between passive study and creative understanding, offering graduate-level introductions to advanced topics in mathematics. The volumes are carefully
Modern Graph Theory