Accession Number : AD0678783

Title :   DISPROOF OF A CONJECTURE OF ERDOS AND MOSER ON TOURNAMENTS,

Corporate Author : ILLINOIS UNIV URBANA

Personal Author(s) : Reid,K. B. ; Parker,E. T.

Report Date : 1964

Pagination or Media Count : 26

Abstract : Erdos and Moser displayed a tournament of order 7 with no transitive subtournament of order 4 and conjectured for each positive integer k existence of a tournament of order 2 superscript (k-1)-1 with no transitive subtournament of order k. The conjecture is disproved for k = 5. Further, every tournament of order 14 has a transitive subtournament of order 5. Inductively, the conjecture is false for all orders above 5. Existence and uniqueness of a tournament of order 13 having no transitive subtournament of order 5 are shown. (Author)

Descriptors :   (*GRAPHICS, SET THEORY), GROUPS(MATHEMATICS), THEOREMS

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE