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Cops and Robbers on Intersection Graphs
[article]

2016
*
arXiv
*
pre-print

The

arXiv:1607.08058v1
fatcat:yyeeioogmbde5hjqtd2tb7proy
*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. ...##
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A Timecop's Chase Around the Table
[article]

2021
*
arXiv
*
pre-print

We consider the

arXiv:2104.08616v2
fatcat:iuyhq5bcgra3dnm6lyh4qgcixm
*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*. ...##
###
Cops and Robbers on Intersection Graphs
[chapter]

2013
*
Lecture Notes in Computer Science
*

The game of

doi:10.1007/978-3-642-45030-3_17
fatcat:k7ojs6vguvhslmropbob6iwnna
*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. ...##
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Cops and Robbers on Toroidal Chess Graphs
[article]

2018
*
arXiv
*
pre-print

Playing it

arXiv:1810.10577v1
fatcat:ju4zp4gfu5bszcdqzqff4gmb4a
*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. ...##
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The capture time of the hypercube
[article]

2013
*
arXiv
*
pre-print

In the game of

arXiv:1308.3354v1
fatcat:qgofi32f6fezpmowoxzgti2rhy
*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*). ...##
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Parameterized pursuit-evasion games

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

doi:10.1016/j.tcs.2010.07.004
fatcat:rqatwvoe7napfii737ce67yyfy
*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*? ...##
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Patterns with Bounded Treewidth
[chapter]

2012
*
Lecture Notes in Computer Science
*

Acknowledgements The authors wish to thank Sanjay Jain

doi:10.1007/978-3-642-28332-1_40
fatcat:ituxrvtoo5fvvk4533iugx26hq
*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*. ...##
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The Capture Time of the Hypercube

2013
*
Electronic Journal of Combinatorics
*

In the game of

doi:10.37236/2921
fatcat:ty5ig2ci5nasvfts43n2xsrmne
*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] . ...##
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Graph Searching in a Crime Wave

2009
*
SIAM Journal on Discrete Mathematics
*

Moreover, we prove an upper bound for mvams(G, r)

doi:10.1137/070705398
fatcat:7dzr6zouznhtpaeyyk7hi7stwy
*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] . ...##
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Constructing Geometric Graphs of Cop Number Three
[article]

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*...

##
###
Catching a fast robber on a grid
[article]

2021
*
arXiv
*
pre-print

We study this model

arXiv:2107.14193v1
fatcat:b54atrvj5bh6zas7tyv37hvcai
*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. ...##
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Algorithmic Decision Optimization Techniques for Multiple Types of Agents with Contrasting Interests
[article]

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

arXiv:0908.0060v1
fatcat:cr7kphwhmzdtrmst6vs2fskjgy
*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 ...##
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Tight Bounds on the Descriptional Complexity of Regular Expressions
[chapter]

2009
*
Lecture Notes in Computer Science
*

We improve

doi:10.1007/978-3-642-02737-6_22
fatcat:zo6ay47qazekvixb2m5flrwlku
*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 ...##
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Subgraphs Satisfying MSO Properties on z-Topologically Orderable Digraphs
[chapter]

2013
*
Lecture Notes in Computer Science
*

closed under taking subgraphs

doi:10.1007/978-3-319-03898-8_12
fatcat:xezphairxffilclt3xlq6hkz74
*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*. ...##
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Watch them Fight! Creativity Task Tournaments of the Swiss Olympiad in Informatics

2016
*
OLYMPIADS IN INFORMATICS
*

The participants can base their solutions

doi:10.15388/ioi.2016.05
fatcat:h3yuli3shfftlepytp6nf5zrpy
*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. ...
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