## Annals of Combinatorics 2 (1998) 137-144k-regular Factors and semi-k-regular Factors in Bipartite Graphs
Keiko Kotani Department of Applied Mathematics, Science University of Tokyo Shinjuku-ku, Tokyo 162-8601, Japan Received April 22, 1998
- Suppose that for each subset
*U*_{1}*X*such that |*U*_{1}|=max{*k*+1, },*G*has an upper semi-*k*-regular factor with defect set*U*_{1}∪*Y*, and for each subset*U*_{2}*Y*such that |*U*_{2}|= max{*k*+1, },*G*has an upper semi-*k*-regular factor with defect set*X*∪*U*_{2}. Then*G*has a*k*-factor. - Suppose that for each subset
*U*_{1}*X*such that |*U*_{1}| = ,*G*has a lower semi-*k*-regular factor with defect set*U*_{1}∪*Y*, and for each subset*U*_{2}*Y*such that |*U*_{2}| = ,*G*has a lower semi-*k*-regular factor with defect set*X*∪*U*_{2}. Then*G*has a*k*-factor.
References
1. A. Kaneko, 2. J. Folkman and D.R. Fulkerson, 3. Keiko Kotani, |