Improved sparse covers for graphs excluding a fixed minor
Costas Busch, Ryan LaFortune, Srikanta Tirthapura · 2007
We consider the construction of sparse covers for planar graphs and other graphs that exclude a fixed minor. We present an algorithm that gives a cover for the γ-neighborhood of each node. For planar graphs, the cover has radius no more than 24γ-8 and degree (maximum cluster overlaps) no more than 18. For every n node graph that excludes a fixed minor, we present an algorithm that yields a cover with radius no more than 4γ and degree O(log n).