
Cops and robbers on oriented graphs
We consider the wellstudied cops and robbers game in the context of ori...
read it

Chromatic Polynomials of Oriented Graphs
The oriented chromatic polynomial of a oriented graph outputs the number...
read it

Oriented coloring on recursively defined digraphs
Coloring is one of the most famous problems in graph theory. The colorin...
read it

On the inversion number of oriented graphs
Let D be an oriented graph. The inversion of a set X of vertices in D co...
read it

Topological Representation of the Transit Sets of kPoint Crossover Operators
kpoint crossover operators and their recombination sets are studied fro...
read it

To reorient is easier than to orient: an online algorithm for reorientation of graphs
We define an online (incremental) algorithm that, given a (possibly inf...
read it

Improved Bounds for the Oriented Radius of Mixed Multigraphs
A mixed multigraph is a multigraph which may contain both undirected and...
read it
A study of cops and robbers in oriented graphs
We consider the wellstudied cops and robbers game in the context of oriented graphs, which has received surprisingly little attention to date. We examine the relationship between the cop numbers of an oriented graph and its underlying undirected graph, giving a surprising result that there exists at least one graph G for which every strongly connected orientation of G has cop number strictly less than that of G. We also refute a conjecture on the structure of copwin digraphs, study orientations of outerplanar graphs, and study the cop number of line digraphs. Finally, we consider some the aspects of optimal play, in particular the capture time of copwin digraphs and properties of the relative positions of the cop(s) and robber.
READ FULL TEXT
Comments
There are no comments yet.