Cycle Decompositions of K_n and K_n - I

Brian Alspach¹
Department of Mathematics and Statistics
Simon Fraser University
Burnaby, British Columbia
Canada V5A 1S6

and

Heather Gavlas
Department of Mathematics
Grand Valley State University
Allendale, Michigan 49401

Abstract:

We establish necessary and sufficient conditions for decomposing the complete graph of even order minus a 1-factor into even cycles and the complete graph of odd order into odd cycles.