We study the expected topological properties of ˇCech and Vietoris-Rips complexes built on random points in Rd . We find higher dimensional analogues of known results for connect...
We determine the exact and asymptotic number of unlabeled outerplanar graphs. The exact number gn of unlabeled outerplanar graphs on n vertices can be computed in polynomial time,...
Let S be a set of n points in IRd and let t > 1 be a real number. A t-spanner for S is a directed graph having the points of S as its vertices, such that for any pair p and q o...
In [13], Erd˝os et al. defined the local chromatic number of a graph as the minimum number of colors that must appear within distance 1 of a vertex. For any ∆ ≥ 2, there are ...
Let S be a set of n points in IRd and let t > 1 be a real number. A t-spanner for S is a directed graph having the points of S as its vertices, such that for any pair p and q o...