Given a drawing of a graph, its visual complexity is defined as the number of geometrical entities in the drawing, for example, the number of segments in a straight-line drawing or the number of arcs in a circular-arc drawing (in 2D). Recently, Chaplick et al. [4] introduced a different measure for the visual complexity, the affine cover number, which is the minimum number of lines (or planes) ...

For a fixed positive integer k, the linear k-arboricity lak(G) of a graph G is the minimum number ` such that the edge set E(G) can be partitioned into ` disjoint sets, each induces a subgraph whose components are paths of lengths at most k. This paper examines linear k-arboricity from an algorithmic point of view. In particular, we present a linear-time algorithm for determining whether a tree...

While the notion of arboricity of a graph is well-known in graph theory, very few results are dedicated to the minimal number of trees covering the edges of a graph, called the tree number of a graph. In this paper we propose a method for computing in polynomial time the tree number of a subclass of planar graphs. The subclass in question includes but is not limited to outerplanar graphs; the d...

Until recently, the fastest distributed MIS algorithm, even for simple graph classes such as unoriented trees that can contain large independent sets within neighborhoods, has been the simple randomized algorithm discovered independently by several researchers in the late 80s. This algorithm (commonly called Luby’s algorithm) computes an MIS of an n-node graph in O(logn) communication rounds (w...