Cycle frames and the Oberwolfach problem

AKCE International Journal of Graphs and Combinatorics

Muthusamy Appu¹  Shanmuga Vadivu Andiyappan¹ 

[1] Department of Mathematics, Periyar University;

关键词: decomposition;    factorization;    cycle frame;   

DOI  :  10.1016/j.akcej.2018.06.008

来源: DOAJ

【 摘 要 】

For an integer denotes a graph with uniform edge-multiplicity Let be a subset of positive integers. A 2-regular subgraph of -partite graph containing vertices of all but one partite set is called partial 2-factor, where denotes wreath product and is an independent set on vertices. If can be partitioned into edge-disjoint partial 2-factors such that each partial 2-factor consists of cycles of lengths from then we say that has a -cycle frame. The Oberwolfach problem OP raised by Ringel, asks the existence of a 2-factorization of (when is odd) or (when is even), in which each 2-factor consists of exactly cycles of length , In this paper, we show that there exists a -cycle frame of if and only if , , . Further we show that there exists a -cycle frame of if and only if and As a consequence, we solve OP OP and OP with some restrictions on

【 授权许可】

Unknown