We propose a definition of locality for properties of geometric graphs. We measure the local density of graphs using region-counting distances [8] between pairs of vertices, and w...
In this paper, we consider the problem of representing graphs by polygons whose sides touch. We show that at least six sides per polygon are necessary by constructing a class of pl...
Emden R. Gansner, Yifan Hu, Michael Kaufmann, Step...
Given a general graph G, a fundamental problem is to find a spanning tree H that best approximates G by some measure. Often this measure is some combination of the congestion and...
We present the first polynomial-time approximation scheme (PTAS) for the Minimum Independent Dominating Set problem in graphs of polynomially bounded growth. Graphs of bounded gr...
The set R of relevant cycles of a graph G is the union of its minimum cycle bases. We introduce a partition of R such that each cycle in a class W can be expressed as a sum of oth...