-An edge of a graph H with a perfect matching is a fixed edge if it either belongs to none or to all of the perfect matchings of H. It is shown that a connected plane bipartite gra...
It is proved that, if G is a K4-minor-free graph with maximum degree 3, then G is totally 4-choosable; that is, if every element (vertex or edge) of G is assigned a list of 4 colo...
In this paper, a structural theorem about toroidal graphs is given that strengthens a result of Borodin on plane graphs. As a consequence, it is proved that every toroidal graph w...
We use Schnyder woods of 3-connected planar graphs to produce convex straight line drawings on a grid of size (n − 2 − ∆) × (n − 2 − ∆). The parameter ∆ ≥ 0 depen...
Suppose we are given a sequence of n points in the Euclidean plane, and our objective is to construct, on-line, a connected graph that connects all of them, trying to minimize the...