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Cops and Robbers on Intersection Graphs [article]

Tomáš Gavenčiak, Przemysław Gordinowicz, Vít Jelínek, Pavel Klavík, Jan Kratochvíl
2016 arXiv   pre-print
The cop number of a graph $G$ is the smallest $k$ such that $k$ cops win the game of cops and robber on $G$.  ...  For more restricted classes of intersection graphs, we obtain better bounds: the maximum cop number of interval filament graphs is two, and the maximum cop number of outer-string graphs is between 3 and  ...  We note that it is proved in [4] that the maximum cop number of unit disk graphs is at most 9. Their strategy is similar to our strategy for string graphs, by applying Lemma 4.3.  ... 
arXiv:1607.08058v1 fatcat:yyeeioogmbde5hjqtd2tb7proy

A Timecop's Chase Around the Table [article]

Nils Morawietz, Petra Wolf
2021 arXiv   pre-print
We consider the cops and robber game variant consisting of one cop and one robber on time-varying graphs (TVG).  ...  Our third main result improves the previously known EXPTIME upper bound for Periodic Cop and Robber on general edge periodic graphs to PSPACE-membership.  ...  We now define the considered cops and robbers variant on edge periodic graphs with one single cop.  ... 
arXiv:2104.08616v2 fatcat:iuyhq5bcgra3dnm6lyh4qgcixm

Cops and Robbers on Intersection Graphs [chapter]

Tomás Gavenčiak, Vít Jelínek, Pavel Klavík, Jan Kratochvíl
2013 Lecture Notes in Computer Science  
The game of cops and robber, introduced by Nowakowski and Winkler in 1983, is played by two players on a graph G, one controlling k cops and the other one robber, all positioned on VG.  ...  In this paper we show an upper bound on the cop-number of string graphs and sharp bounds on the cop-number of interval filament graphs, circular graphs, circular arc graphs and function graphs.  ...  The cop number of a graph G is the minimum number k of cops such that Player One has a winning strategy with k cops on G. Known Results.  ... 
doi:10.1007/978-3-642-45030-3_17 fatcat:k7ojs6vguvhslmropbob6iwnna

Cops and Robbers on Toroidal Chess Graphs [article]

Allyson Hahn, Neil R. Nicholson
2018 arXiv   pre-print
Playing it on an $n \times n$ toroidal chess graph, the game is varied by defining moves for cops and robbers differently, always mimicking moves of certain chess pieces.  ...  We investigate multiple variants of the game Cops and Robbers.  ...  The research done here was completed prior to one author (Hahn) taking an introduction-to-proofs course.  ... 
arXiv:1810.10577v1 fatcat:ju4zp4gfu5bszcdqzqff4gmb4a

The capture time of the hypercube [article]

Anthony Bonato, William B. Kinnersley, P. Gordinowicz, P. Pralat
2013 arXiv   pre-print
In the game of Cops and Robbers, the capture time of a graph is the minimum number of moves needed by the cops to capture the robber, assuming optimal play.  ...  For additional background on Cops and Robbers and Meyniel's conjecture, see the book [3] .  ...  The cops win if after some finite number of rounds, one of them can occupy the same vertex as the robber (in a reflexive graph, this is equivalent to the cop landing on the robber).  ... 
arXiv:1308.3354v1 fatcat:qgofi32f6fezpmowoxzgti2rhy

Parameterized pursuit-evasion games

Allan Scott, Ulrike Stege
2010 Theoretical Computer Science  
We now review the definition of the problem Unitary Parameterized QBFSAT 2 , which is known to be AW[*]complete [1]. 3 1 Note that we say the cops and robber may move, but they can also stay at the vertex  ...  A-hierarchy is in turn a superset of the corresponding W-hierarchy 2 class (that is, W[t] ⊆ A[t] for t ≥ 1), and W[1] contains FPT.  ...  k cops can capture the robber?  ... 
doi:10.1016/j.tcs.2010.07.004 fatcat:rqatwvoe7napfii737ce67yyfy

Patterns with Bounded Treewidth [chapter]

Daniel Reidenbach, Markus L. Schmid
2012 Lecture Notes in Computer Science  
Acknowledgements The authors wish to thank Sanjay Jain and the anonymous referees for their detailed and helpful remarks and suggestions, which will be taken into account for the full version of this paper  ...  If k = 1, then 3 cops are sufficient to catch a robber on the Gaifman graph of A s α , and if k ≥ 2, then k + 1 cops are sufficient to catch a robber on the Gaifman graph of A s α .  ...  In the robber-cops-game (called jump searching in [17] ), a number of cops try to catch a robber on a graph. Let G := (V, E) be a graph.  ... 
doi:10.1007/978-3-642-28332-1_40 fatcat:ituxrvtoo5fvvk4533iugx26hq

The Capture Time of the Hypercube

Anthony Bonato, Przemysław Gordinowicz, Bill Kinnersley, Paweł Prałat
2013 Electronic Journal of Combinatorics  
In the game of Cops and Robbers, the capture time of a graph is the minimum number of moves needed by the cops to capture the robber, assuming optimal play.  ...  For background on graph theory, the reader is directed to [13] . The game of Cops and Robbers was independently introduced in [11, 12] and the cop number was introduced in [1] .  ...  For additional background on Cops and Robbers and Meyniel's conjecture, see the book [3] .  ... 
doi:10.37236/2921 fatcat:ty5ig2ci5nasvfts43n2xsrmne

Graph Searching in a Crime Wave

David Richerby, Dimitrios M. Thilikos
2009 SIAM Journal on Discrete Mathematics  
Moreover, we prove an upper bound for mvams(G, r) on general graphs and show that this bound is reached by an infinite class of graphs.  ...  Our model is defined for robbers that are visible (their position in the graph is known to the cops) and active (they can move at any point in the game) but is easily adapted to other variants of the single-robber  ...  One of the main models of graph searching, known as the helicopter cops and robber game, was introduced by Seymour and Thomas [11] .  ... 
doi:10.1137/070705398 fatcat:7dzr6zouznhtpaeyyk7hi7stwy

Constructing Geometric Graphs of Cop Number Three [article]

Seyyed Aliasghar Hosseini, Masood Masjoody, Ladislav Stacho
2019 arXiv   pre-print
Cops and robbers has been studies on several classes of graphs including geometrically represented graphs.  ...  The game of cops and robbers is a pursuit game on graphs where a set of agents, called the cops try to get to the same position of another agent, called the robber.  ...  Introduction A game of cops and robbers is a pursuit game on graphs, or a class of graphs, in which a set of agents, called the cops, try to get to the same position as another agent, called the robber  ... 
arXiv:1811.04338v2 fatcat:5amsjeryhrbq3hlvdywkf3l2zm

Catching a fast robber on a grid [article]

William B. Kinnersley, Nikolas Townsend
2021 arXiv   pre-print
We study this model on several classes of grid-like graphs.  ...  We consider a variant of Cops and Robbers in which the robber may traverse as many edges as he likes in each turn, with the constraint that he cannot pass through any vertex occupied by a cop.  ...  Introduction Cops and Robbers is a well-studied model of pursuit and evasion in which a team of one or more cops attempts to capture a single robber on a graph G.  ... 
arXiv:2107.14193v1 fatcat:b54atrvj5bh6zas7tyv37hvcai

Algorithmic Decision Optimization Techniques for Multiple Types of Agents with Contrasting Interests [article]

Mugurel Ionut Andreica
2009 arXiv   pre-print
The interactions between the agents are modelled by using several types of two-player games, where the agents have identical roles and compete for the same resources, or where they have different roles  ...  The described situations have applications in modelling behavior in many types of environments, like distributed systems, learning environments, resource negotiation environments, and many others.  ...  AGENT PURSUING GAMES ON GRAPHS PURSUING A SET OF ROBBERS In a directed graph with n vertices and m edges there are A cop agents (cops) and B robber agents (robbers): every cop i is initially located  ... 
arXiv:0908.0060v1 fatcat:cr7kphwhmzdtrmst6vs2fskjgy

Tight Bounds on the Descriptional Complexity of Regular Expressions [chapter]

Hermann Gruber, Markus Holzer
2009 Lecture Notes in Computer Science  
We improve on some recent results on lower bounds for conversion problems for regular expressions.  ...  , and the conversion of regular expressions extended by adding intersection or interleaving to ordinary regular expressions.  ...  It was shown in [17] that on the graph G k , the robber has a winning strategy against k cops in the cops and strong visible robber game, even if the cops are not immutable and can freely jump between  ... 
doi:10.1007/978-3-642-02737-6_22 fatcat:zo6ay47qazekvixb2m5flrwlku

Subgraphs Satisfying MSO Properties on z-Topologically Orderable Digraphs [chapter]

Mateus de Oliveira Oliveira
2013 Lecture Notes in Computer Science  
closed under taking subgraphs and whose constant levels incorporate families of graphs of arbitrarily large undirected tree-width and arbitrarily large clique width.  ...  Our result implies the polynomial time solvability of many natural counting problems on digraphs admitting z-topological orderings for constant values of z and k.  ...  A cops-and-robber game on G is played by two parties. One is controlling a set of k cops and the other is controlling a robber.  ... 
doi:10.1007/978-3-319-03898-8_12 fatcat:xezphairxffilclt3xlq6hkz74

Watch them Fight! Creativity Task Tournaments of the Swiss Olympiad in Informatics

Samuel GRÜTTER, Daniel GRAF, Benjamin SCHMID
The participants can base their solutions on these sample bots to quickly learn how to implement the protocol and input/output.  ...  At the start of each year's first round, the following material for the creativity task is published on the SOI website: The • task description, describing the rules of the game and its parameters.  ...  A game of cops and robbers. Discrete Applied Mathematics, 8(1), 1-12. Burton, B. (2008) . Breaking the routine: events to complement Informatics Oly training. Olympiads in Informatics, 2, 5-15.  ... 
doi:10.15388/ioi.2016.05 fatcat:h3yuli3shfftlepytp6nf5zrpy
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