Sugeng, Mardiyono
(1998)
*SOME NECESSARY AND SUFFICIENT CONDITIONS ON ALMOST REGULAR GRAPHS WITHOUT ONE-FACTORS.*
[Experiment/Research]

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## Abstract

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.

Item Type: | Experiment/Research |
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Subjects: | LPPM |

Divisions: | LPPM - Lembaga Penelitian dan Pengabdian kepada Masyarakat |

Date Deposited: | 17 Sep 2012 08:26 |

Last Modified: | 02 Oct 2019 02:16 |

URI: | http://eprints.uny.ac.id/id/eprint/5665 |

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