# Even flying cops should think ahead

@article{Martinsson2018EvenFC, title={Even flying cops should think ahead}, author={A. Martinsson and Florian Meier and P. Schnider and A. Steger}, journal={ArXiv}, year={2018}, volume={abs/1801.07193} }

We study the entanglement game, which is a version of cops and robbers, on sparse graphs. While the minimum degree of a graph G is a lower bound for the number of cops needed to catch a robber in G, we show that the required number of cops can be much larger, even for graphs with small maximum degree. In particular, we show that there are 3-regular graphs where a linear number of cops are needed.

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SHOWING 1-10 OF 20 REFERENCES

A game of cops and robbers

- Computer Science, Mathematics
- Discret. Appl. Math.
- 1984

It is shown that there are graphs on which arbitrarily many cops are needed to catch the robber and it is proved that for planar graphs 3 cops always suffice to win. Expand

Lazy Cops and Robbers played on random graphs and graphs on surfaces

- Mathematics
- 2016

We consider a variant of the game of Cops and Robbers, called Lazy Cops and Robbers, where at most one cop can move in any round. The lazy cop number is the analogue of the usual cop number for this… Expand

Chasing a Fast Robber on Planar Graphs and Random Graphs

- Mathematics, Computer Science
- J. Graph Theory
- 2015

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… Expand

Variations on cops and robbers

- Mathematics, Computer Science
- J. Graph Theory
- 2012

The directed graph version of the classical Cops and Robbers game is studied, and it is shown that the cop number of any strongly connected digraph on n vertices is O(n(loglogn)2/logn). Expand

Lazy Cops and Robbers played on Graphs

- Mathematics
- 2013

We consider a variant of the game of Cops and Robbers, called Lazy Cops and Robbers, where at most one cop can move in any round. We investigate the analogue of the cop number for this game, which we… Expand

Entanglement - A Measure for the Complexity of Directed Graphs with Applications to Logic and Games

- Computer Science
- LPAR
- 2004

We propose a new parameter for the complexity of finite directed graphs which measures to what extent the cycles of the graph are intertwined. This measure, called entanglement, is defined by way of… Expand

Cops and Robbers from a distance

- Computer Science, Mathematics
- Theor. Comput. Sci.
- 2010

It is proved that (nk)^1/^2^+^o^(^1^)@?c"k(n)=O(nlog(2nk+1)log(k+2)k-1), where c"k (n) is the maximum of c"K(G) over all n-vertex connected graphs. Expand

Vertex-to-vertex pursuit in a graph

- Computer Science, Mathematics
- Discret. Math.
- 1983

This work characterize the graphs on which the cop has a winning strategy, and connects the problem with the structure theory of graphs based on products and retracts. Expand

Entanglement and the complexity of directed graphs

- Mathematics, Computer Science
- Theor. Comput. Sci.
- 2012

It is established that the complexity of solving a parity game can be parametrised in terms of the minimal entanglement of subgames induced by a winning strategy and one of the main results is that parity games of boundedEntanglement can be solved in polynomial time. Expand

A Probabilistic Proof of an Asymptotic Formula for the Number of Labelled Regular Graphs

- Mathematics, Computer Science
- Eur. J. Comb.
- 1980

The method determines the asymptotic distribution of the number of short cycles in graphs with a given degree sequence, and gives analogous formulae for hypergraphs. Expand