We show that any face hitting set of size n of a connected planar graph with a minimum degree of at least 3 is contained in a connected subgraph of size 5n − 6. Furthermore we s...
Let TS be the set of all crossing-free straight line spanning trees of a planar n-point set S. Consider the graph TS where two members T and T of TS are adjacent if T intersects T...
Oswin Aichholzer, Franz Aurenhammer, Clemens Hueme...
The unit ball random geometric graph G = Gd p(λ, n) has as its vertices n points distributed independently and uniformly in the unit ball in Rd, with two vertices adjacent if and ...
Robert B. Ellis, Jeremy L. Martin, Catherine H. Ya...
We maintain the maximum spanning tree of a planar point set, as points are inserted or deleted, in O(log3 n) time per update in Mulmuley's expected-case model of dynamic geom...
: Both the pancake graph and star graph are Cayley graphs and are especially attractive for parallel processing. They both have sublogarithmic diameter, and are fairly sparse compa...