10 citations · 17 across the 6 of their papers we have counts for
6 papers · 1 filter
Cops and Robbers on graphs of bounded diameter
Seyyed Aliasghar Hosseini, Fiachra Knox, Bojan Mohar
The game of Cops and Robbers is a well known game played on graphs. In this paper we consider the class of graphs of bounded diameter. We improve the strategy of cops and previousl…
Meyniel's conjecture on graphs of bounded degree
Seyyed Aliasghar Hosseini, Bojan Mohar, Sebastian Gonzalez Hermosillo de la Maza
The game of Cops and Robbers is a well known pursuit-evasion game played on graphs. It has been proved \cite{bounded_degree} that cubic graphs can have arbitrarily large cop number…
Surrounding cops and robbers on graphs of bounded genus
Peter Bradshaw, Seyyed Aliasghar Hosseini
We consider a surrounding variant of cops and robbers on graphs of bounded genus. We obtain bounds on the number of cops required to surround a robber on planar graphs, toroidal gr…
Cops and robbers on directed and undirected abelian Cayley graphs
Peter Bradshaw, Seyyed Aliasghar Hosseini, Jérémie Turcotte
We show that the cop number of directed and undirected Cayley graphs on abelian groups has an upper bound of the form of , where is the number of vertices, by intr…
Vertex arboricity of cographs
Sebastián González Hermosillo de la Maza, Pavol Hell, César Hernández Cruz +2
Arboricity is a graph parameter akin to chromatic number, in that it seeks to partition the vertices into the smallest number of sparse subgraphs. Where for the chromatic number we…
Cops and robbers on oriented toroidal grids
Sebastian Gonzalez Hermosillo de la Maza, Seyyed Aliasghar Hosseini, Fiachra Knox +2
The game of cops and robbers is a well-known game played on graphs. In this paper we consider the straight-ahead orientations of 4-regular quadrangulations of the torus and the Kle…