A k-frugal colouring of a graph G is a proper colouring of the vertices of G such that no colour appears more than k times in the neighbourhood of a vertex. This type of colouring...
An upper bound for the domination number of the direct product of graphs is proved. It in particular implies that for any graphs G and H, γ(G × H) ≤ 3γ(G)γ(H). Graphs with a...
We consider planning optimal collision-free motions of two polygonal robots under translation. Each robot has a reference point that must lie on a given graph, called a roadmap, w...
Hamid Reza Chitsaz, Steven M. LaValle, Jason M. O'...
Vertex pursuit games, such as the game of Cops and Robbers, are a simplified model for network security. In these games, cops try to capture a robber loose on the vertices of the ...
— Motion planning for robotic arms is important for real, physical world applications. The planning for arms with high-degree-of-freedom (DOF) is hard because its search space is...