Let D be a set of positive integers. The distance graph generated by D, denoted by G(Z, D), has the set Z of all integers as the vertex Supported in part by the National Science ...
Let G = (V, E) be a simple graph on vertex set V and define a function f : V {-1, 1}. The function f is a signed dominating function if for every vertex x V, the closed neighbor...
We prove that for sufficiently large n, there exist unit disk graphs on n vertices such that for every representation with disks in the plane at least c √ n bits are needed to wr...
: Let G be a graph on n vertices in which every induced subgraph on s = log3 n vertices has an independent set of size at least t = log n. What is the largest q = q(n) so that ever...
: In this paper, we study spectral versions of the densest subgraph problem and the largest independence subset problem. In the first part, we give an algorithm for identifying sm...