Let P(n, k) denote the number of graphs on n + k vertices that contain Pn, a path on n vertices, as an induced subgraph. In this note we will find upper and lower bounds for P(n, ...
This work introduces new bounds on the clique number of graphs derived from a result due to S´os and Straus, which generalizes the Motzkin-Straus Theorem to a specific class of h...
We consider a planning problem that generalizes Alcuin's river crossing problem (also known as: The wolf, goat, and cabbage puzzle) to scenarios with arbitrary conflict graph...
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 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...