A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is `application/pdf`

.

## Filters

##
###
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*. ... (Unlike in interval*graphs*where edges only*on**intersections*of [a, b]*and*[c, d].) ...##
###
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 instance, we show that the*cop*number is unbounded*on**intersection**graphs*of two-element subsets of a line, as well as*on**intersection**graphs*of 3-dimensional unit balls, of 3-dimensional unit cubes ... 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. ...##
###
Cop and Robber Games When the Robber Can Hide and Ride

2011
*
SIAM Journal on Discrete Mathematics
*

In the classical

doi:10.1137/100784035
fatcat:j7hm3mnjwnerpfr6jeydniiuzm
*cop**and**robber*game, two players, the*cop*C*and*the*robber*R, move alternatively along edges of a finite*graph*G = (V, E). ... The*cop*captures the*robber*if both players are*on*the same vertex at the same moment of time. A*graph*G is called*cop*win if the*cop*always captures the*robber*after a finite number of steps. ... Vaxès,*Cop**and**robber*games when the*robber*can hide*and*ride, arXiv:1001.4457. inria-00482117, version 1 -9 May 2010 Author manuscript, published in "8th French Combinatorial Conference (2010)" ...##
###
Most Generalized Petersen graphs of girth 8 have cop number 4
[article]

2020
*
arXiv
*
pre-print

Even more generally, in a

arXiv:2009.00693v1
fatcat:ugsx754ksbhmnfcl3k6k53q5fi
*graph*of girth at least $9$*and*minimum valency $\delta$, the*cop*number is at least $\delta+1$. ... A generalized Petersen*graph*$GP(n,k)$ is a regular cubic*graph**on*$2n$ vertices (the parameter $k$ is used to define some of the edges). ...*Cops**and**robbers*is a pursuit-evasion game played*on**graphs*[13, 14] by two players*on*a simple*graph*G. ...##
###
Pursuit-evasion games on latin square graphs
[article]

2021
*
arXiv
*
pre-print

We investigate various pursuit-evasion parameters

arXiv:2109.14669v1
fatcat:3i7gzaexp5a3dmrrqqvkp5y7je
*on*latin square*graphs*, including the*cop*number, metric dimension,*and*localization number. ... The*cop*number of latin square*graphs*is studied,*and*for $k$-MOLS$(n),$ bounds for the*cop*number are given. ... The fifth author was supported by funds from NSERC*and*The Fields Institute for Research in Mathematical Sciences. ...##
###
Localization game on geometric and planar graphs
[article]

2017
*
arXiv
*
pre-print

The model we introduce is based

arXiv:1709.05904v1
fatcat:prmk5irozzby3etqieay5tzw6i
*on*a pursuit*graph*game that resembles the famous*Cops**and**Robbers*game. It can be considered as a game theoretic variant of the \emph{metric dimension} of a*graph*. ... We provide upper bounds*on*the related*graph*invariant $\zeta (G)$, defined as the least number of*cops*needed to localize the*robber**on*a*graph*$G$, for several classes of*graphs*(trees, bipartite*graphs*... If these cycles*intersect*in only*one*point, this is the location of the*robber**and*the*Cop*-player wins. ...##
###
Cops, Robber and Medianwidth Parameters
[article]

2016
*
arXiv
*
pre-print

We study a generalisation of the classical

arXiv:1603.06871v1
fatcat:djtdhw6kyjfsbj23mademzeyam
*Cops**and**Robber*game, where the*robber*plays against not just*one*, but $i$*cop*players. ... We characterise the $i$-latticewidth of a*graph*in terms of maximal*intersections*of bags of $i$ path decompositions of the*graph*. ... The game is played*on*a finite, undirected*graph*G by the*cop*player, who controls k*cops*,*and*the*robber*player. ...##
###
The localization number and metric dimension of graphs of diameter 2
[article]

2020
*
arXiv
*
pre-print

We consider the localization number

arXiv:2008.04896v1
fatcat:ngrs32itxvg5dhmkuweteahskm
*and*metric dimension of certain*graphs*of diameter $2$, focusing*on*families of Kneser*graphs**and**graphs*without 4-cycles. ... We determine bounds*on*the localization number*and*metric dimension of Moore*graphs*of diameter $2$*and*polarity*graphs*. ... For more*on*polarity*graphs*, see [27] . Polarity*graphs*were studied for the game of*Cops**and**Robbers*in [5] , where bounds were given*on*the*cop*number. ...##
###
Vertex-to-vertex pursuit in a graph

1983
*
Discrete Mathematics
*

We characterize the

doi:10.1016/0012-365x(83)90160-7
fatcat:5wey2cd3endebbp2qudybypuom
*graphs**on*which the*cop*has a winning strategy,*and*connect the problem with the structure theory of*graphs*based*on*products*and*retracts. ... A*graph*G is given*and*two players, a*cop**and*a*robber*, play the folioking game: the*cop*chooses a vertex, then the*robber*chooses a vertex, then the players move alternately beginning with the*cop*. ... The*cop*plays his winning strategy*on*each Gi ; once he catches the*robber**on**one**graph*, he can stay with his quarry until he has won all n games*and*is now*on*the sa.me vertex as the*robber**on*the product ...##
###
A note on bounds for the cop number using tree decompositions
[article]

2013
*
arXiv
*
pre-print

In this short note, we supply a new upper bound

arXiv:1308.2839v1
fatcat:ijqewc43sfd5pftpfiy3oukeki
*on*the*cop*number in terms of tree decompositions. Our results in some cases extend a previously derived bound*on*the*cop*number using treewidth. ... For additional background*on**Cops**and**Robbers**and*Meyniel's conjecture, see the recent 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*). ...##
###
The Robber Strikes Back
[chapter]

2013
*
Advances in Intelligent Systems and Computing
*

We study the minimum number of

doi:10.1007/978-81-322-1680-3_1
fatcat:lqyeq446gjffjf3d5vxbmwnofe
*cops*needed to capture a*robber**on*a*graph*G, written cc(G). ... We give bounds*on*cc(G) in terms of the*cop*number of G in the classes of bipartite*graphs**and*diameter two, K1,m-free*graphs*. ... The*cops**and**robber*occupy vertices,*and*more than*one**cop*may occupy a vertex. ...##
###
The robber strikes back
[article]

2013
*
arXiv
*
pre-print

We study the minimum number of

arXiv:1308.2843v1
fatcat:tql2g4fr6fgglgdkq6edpon5w4
*cops*needed to capture a*robber**on*a*graph*$G$, written $cc(G)$. ... We give bounds*on*$cc(G)$ in terms of the*cop*number of $G$ in the classes of bipartite*graphs**and*diameter two, $K_{1,m}$-free*graphs*. ... The*cops**and**robber*occupy vertices,*and*more than*one**cop*may occupy a vertex. ...##
###
A Timecop's Work Is Harder Than You Think

2020
*
International Symposium on Mathematical Foundations of Computer Science
*

We consider the (parameterized) complexity of a

doi:10.4230/lipics.mfcs.2020.71
dblp:conf/mfcs/MorawietzRW20
fatcat:agic5zj7tfcrzfkk2abwaajitu
*cop**and**robber*game*on*periodic, temporal*graphs**and*a problem*on*periodic sequences to which these games relate intimately. ... As*one*main result we show that even if the*graph*has a size-2 vertex cover*and*is acyclic in each time step, the*cop**and**robber*game*on*periodic, temporal*graphs*is NP-hard*and*W[1]-hard when parameterized ... Our hardness results are based*on*intuitive algebraic problems called Periodic Character Alignment*and*Periodic Full Character Alignment, asking whether a given set of periodic sequences over {0, 1} is ...##
###
Visibility graphs, dismantlability, and the cops and robbers game

2017
*
Computational geometry
*

We study versions of

doi:10.1016/j.comgeo.2017.07.001
fatcat:7hguik3t4bdyzimgo6rr6mrxhu
*cop**and**robber*pursuit-evasion games*on*the visibility*graphs*of polygons,*and*inside polygons with straight*and*curved sides. ... In visibility*graphs*we show the*cop*can always win because visibility*graphs*are dismantlable, which is interesting as*one*of the few results relating visibility*graphs*to other known*graph*classes. ... Acknowledgements The*cops**and**robbers*problem for points inside a region with a curved boundary was initially suggested by Vinayak Pathak*and*was posed in the Open Problem Session of CCCG 2013 by the third ...##
###
Fast Robber in Planar Graphs
[chapter]

2008
*
Lecture Notes in Computer Science
*

In the

doi:10.1007/978-3-540-92248-3_28
fatcat:vc6l4jdacfe67b7anhlnu4zjwe
*cops**and**robber*game, two players play alternately by moving their tokens along the edges of a*graph*. The first*one*plays with the*cops**and*the second*one*with*one**robber*. ... If the*cops**and*the*robber*have the same velocity, 3 + 3 2 g*cops*are sufficient to capture*one**robber*in any*graph*with genus g (Schröder, 2001). ... Add a universal vertex u to G*and*denote the resulting*graph*by H. Catching the*robber*in C 4 takes 2*cops*, whereas just*one**cop*placed*on*u in H does the job in*one*move. ...
« Previous

*Showing results 1 — 15 out of 321 results*