We consider the problem of periodic graph exploration by a finite automaton in which an automaton with a constant number of states has to explore all unknown anonymous graphs of a...
Given an integer s 0 and a permutation Sn, let ,s be the graph on n vertices {1, . . . , n} where two vertices i < j are adjacent if the permutation flips their order and th...
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, ...
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...