The linear-width of a graph G is de ned to be the smallest integer k such that the edges of G can be arranged in a linear ordering e1;:::;er in such a way that for every i = 1;:::...
We study properties of the sets of minimal forbidden minors for the families of graphs having a vertex cover of size at most k. We denote this set by O(k-VERTEX COVER) and call it...
A permutation graph is an intersection graph of segments lying between two parallel lines. A Seidel complementation of a finite graph at a vertex v consists in complementing the ed...
A map is a graph equipped with a circular order of edges around each vertex. These circular orders represent local planar embeddings. The genus of a map is the minimal genus of an...
We construct algorithms for deciding essentially any minor-closed parameter, with explicit time bounds. This result strengthens previous results by Robertson and Seymour [1,2], Fr...