%0 Generic
%A Sugeng, Mardiyono
%A FACULTY OF MATHEMATICS AND SCIENCE EDUCATION,
%D 1998
%F UNY:5665
%T SOME NECESSARY AND SUFFICIENT CONDITIONS ON ALMOST REGULAR GRAPHS WITHOUT ONE-FACTORS
%U http://eprints.uny.ac.id/5665/
%X 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.