Let P(n, k) denote the number of graphs on n + k vertices that contain Pn, a path on n vertices, as an induced subgraph. In this note we will find upper and lower bounds for P(n, ...
We present an expected polynomial time algorithm to generate a 2-connected unlabeled planar graph uniformly at random. To do this we first derive recurrence formulas to count the ...
Given an n-vertex graph G, a drawing of G in the plane is a mapping of its vertices into points of the plane, and its edges into continuous curves, connecting the images of their ...
Julia Chuzhoy, Yury Makarychev, Anastasios Sidirop...
For a bounded integer , we wish to color all edges of a graph G so that any two edges within distance have different colors. Such a coloring is called a distance-edge-coloring or ...
Suppose we are given a graph G together with two proper vertex k-colourings of G, α and β. How easily can we decide whether it is possible to transform α into β by recolouring...