The aim of this note is to point out some combinatorial applications of a lemma of Scarf, proved first in the context of game theory. The usefulness of the lemma in combinatorics...
A system of linear equations in p unknowns Mx = b is said to have the removal property if every set S ⊆ {1, . . . , n} which contains o(np− ) solutions of Mx = b can be turned...
Abstract— Thorup and Zwick, in their seminal work, introduced the approximate distance oracle, which is a data structure that answers distance queries in a graph. For any integer...
Let H be a fixed directed graph on h vertices, let G be a directed graph on n vertices and suppose that at least n2 edges have to be deleted from it to make it H-free. We show tha...
A combinatorial channel is a set of pairs of words describing all the possible input-output channel situations. We introduce the concept "maximal error-detecting capability&q...