Probabilistic Roadmaps (PRM) are a commonly used class of algorithms for robot navigation tasks where obstacles are present in the environment. We examine the situation where the ...
We investigate the notion of quantum chromatic number of a graph, which is the minimal number of colours necessary in a protocol in which two separated provers can convince a refe...
Peter J. Cameron, Ashley Montanaro, Michael W. New...
A set of vertices C in a graph is convex if it contains all vertices which lie on shortest paths between vertices in C. The convex hull of a set of vertices S is the smallest conve...
An overlap representation is an assignment of sets to the vertices of a graph in such a way that two vertices are adjacent if and only if the sets assigned to them overlap. The ov...
The k-domination number of a graph is the cardinality of a smallest set of vertices such that every vertex not in the set is adjacent to at least k vertices of the set. We prove t...