Ramsey-type results for Gallai colorings * Andr´asGy´arf´ as † Computer and Automation Research Institute Hungarian Academy of Sciences Budapest, P.O. Box 63 Budapest, Hungary, H-1518 gyarfas@sztaki.hu G´aborN.S´ark¨ ozy ‡ Computer Science Department Worcester Polytechnic Institute Worcester, MA, USA 01609 gsarkozy@cs.wpi.edu and Computer and Automation Research Institute Hungarian Academy of Sciences Budapest, P.O. Box 63 Budapest, Hungary, H-1518 Stanley Selkow Computer Science Department Worcester Polytechnic Institute Worcester, MA, USA 01609 sms@cs.wpi.edu July 21, 2008 * 2000 Mathematics Subject Classification: 05C15, 05C35, 05C55. † Research supported in part by OTKA Grant No. K68322. ‡ Research supported in part by OTKA Grant No. K68322. 1