We explore the average-case “Vickrey” cost of structures in a random setting: the Vickrey cost of a shortest path in a complete graph or digraph with random edge weights; the V...
For digraphs D and H, a mapping f : V (D)V (H) is a homomorphism of D to H if uv A(D) implies f(u)f(v) A(H). For a fixed directed or undirected graph H and an input graph D, the...
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...
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...