Given a graph G of order n containing no C-4, color an edge e of the c
omplement of G red if G + e contains a C-4, and blue otherwise. Among
other results, we answer a question of Erdos, de la Vina, and Fajtlowi
cz by showing that neither the red nor the blue graph obtained need co
ntain a large complete subgraph. (C) 1998 John Wiley & Sons, Inc.