Autumn Colorations

Imbalances in k-colorations

1. INTRODUCTION The following problem is due to Paul Erdijs tll. Color the edges of a complete graph K on n vertices red and blue. What n is the largest t such that we may always find a complete subgraph in which I# red edges-# blue edges1 Lt? We need a more precise and more general formulation. For any set V, define Vk = {W :, w&V, Iwl = k). (1) Note that V2 is the complete graph generated by ...

Quadrangulations and 2-colorations

Any metric quadrangulation (made by segments of straight line) of a point set in the plane determines a 2-coloration of the set, such that edges of the quadrangulation can only join points with different colors. In this work we focus in 2-colorations and study whether they admit a quadrangulation or not, and whether, given two quadrangulations of the same 2-coloration, it is possible to carry o...

Autumn spring.

artists; signatures and monograms, an international directory. Castagno, John. Scarecrow Pr., ©2007 567 p. $225.00 Castagno, a multimedia artist and sculptor and author of other books in the Artists’ Signatures and Monograms series, presents a reference for identifying, authenticating, and verifying signatures and works of wellknown and little-known abstract artists. About 2,300 painters, print...

, Autumn 2013

Forcing Colorations and the Strong Perfect Graph Conjecture

We give various reformulations of the Strong Perfect Graph Conjecture, based on a study of forced coloring procedures, uniquely colorable subgraphs and ! ? 1-cliques in minimal imperfect graphs.