TY  - GEN
UR  - http://eprints.uny.ac.id/5665/
ID  - UNY5665
AV  - public
TI  - SOME NECESSARY AND SUFFICIENT CONDITIONS ON ALMOST REGULAR GRAPHS WITHOUT ONE-FACTORS
A1  - Sugeng, Mardiyono
Y1  - 1998///
N2  - A one-factor of a graph G is a I-regular spanning subgraph of G. For given positive integers and even e, let qc(2n;d,e,t) be the class of simple connected graphs on 2d vertiqes, (2n-k) of which have degree d and k has degree d+e, having exactly t one-factors.!Recently, W.D. Wallis asked for what value of n is qt(2n;d,e,O) 'I: 0? This problem has been completely solved by Caccetta and Mardiyono (1994). However, the next problem is : can we establish some necessary and sufficient conditions 9n G E qt(2n;d,e,O) for 2n =3d+I, 2n = 3d+3 and 2n =3d+5 whenever d is odd, and for 2n =3d+4 whenever d is even. In this paper we establish some necessary and sufficient conditions on G E qt(2n;d,e,O) for 2n =3d+I, 2n =3d+3 and2n=3dr+-5whenever d is odd, and for 2n =3d+4wheneverd is even.
ER  -