Two-Factors Each Component of Which Contains a Specified Vertex Yoshimi Egawa, 1 Hikoe Enomoto, 2 Ralph J. Faudree, 3 Hao Li, 4 and Ingo Schiermeyer 5 * 1 DEPARTMENT OF APPLIED MATHEMATICS SCIENCE UNIVERSITY OF TOKYO TOKYO 162-8601, JAPAN 2 DEPARTMENT OF MATHEMATICS KEIO UNIVERSITY YOKOHAMA 223-8522, JAPAN 3 DEPARTMENT OF MATHEMATICAL SCIENCES UNIVERSITY OF MEMPHIS MEMPHIS, TENNESSEE 38152 4 LRI, URA 410 DU CNRS UNIVERSITE ´ PARIS-SUD 91405 ORSAY CEDEX, FRANCE 5 FAKULTA ¨ T FU ¨ R MATHEMATIK UND INFORMATIK TECHNISCHE UNIVERSITA ¨ T BERGAKADEMIE FREIBERG 09596 FREIBERG, GERMANY E-mail: schierme@mathe.tu-freiberg.de Received December 13, 2000; Revised December 4, 2002 —————————————————— *Correspondence to: Ingo Schiermeyer, Inst. f. Theor. Mathematik, TU Bergaka- demie Freiberg, Agricolastr. 1, 09596 Freiberg, Germany. E-mail: schierme@mathe.tu-freiberg.de ß 2003 Wiley Periodicals, Inc.