We give a very short proof of the following result of Graham from 1980: For any finite coloring of Rd , d 2, and for any > 0, there is a monochromatic (d + 1)-tuple that span...
A homomorphism from an oriented graph G to an oriented graph H is a mapping from the set of vertices of G to the set of vertices of H such that -----(u)(v) is an arc in H whenever...
A homomorphism from an oriented graph G to an oriented graph H is an arc-preserving mapping from V (G) to V (H), that is (x)(y) is an arc in H whenever xy is an arc in G. The orie...
In the well-studied Majority problem, we are given a set of n balls colored with two or more colors, and the goal is to use the minimum number of color comparisons to find a ball ...
Fan R. K. Chung, Ronald L. Graham, Jia Mao, Andrew...
A graph is f-choosable if for every collection of lists with list sizes specified by f there is a proper coloring using colors from the lists. The sum choice number is the minimum...