For any graph G, the k-improper chromatic number k (G) is the smallest number of colours used in a colouring of G such that each colour class induces a subgraph of maximum degree ...
Because of irreversibility of movements, motion planning on directed graphs is much more intricate than that on graphs. Recently we showed that the feasibility of motion planning o...
The number of matchings of a graph G is an important graph parameter in various contexts, notably in statistical physics (dimer-monomer model). Following recent research on graph p...
For a graph G, let fij be the number of spanning rooted forests in which vertex j belongs to a tree rooted at i. In this paper, we show that for a path, the fij's can be expr...
Large graphs are difficult to browse and to visually explore. This note adds up evidence that some graph drawing techniques, which produce readable layouts when applied to medium-s...