期刊名称：AKCE International Journal of Graphs and Combinatorics
印刷版ISSN：0972-8600
出版年度：2019
卷号：16
期号：1
页码：83-95
DOI：10.1016/j.akcej.2018.06.008
语种：English
出版社：Elsevier
摘要：AbstractFor an integerλ,G(λ)denotes a graphGwith uniform edge-multiplicityλ.LetJbe a subset of positive integers. A 2-regular subgraph ofm-partite graphKm⊗Incontaining vertices of all but one partite set is calledpartial 2-factor, where⊗denotes wreath product andInis an independent set onnvertices. If(Km⊗In)(λ)can be partitioned into edge-disjoint partial 2-factors such that each partial 2-factor consists of cycles of lengths fromJ,then we say that(Km⊗In)(λ)has a(J,λ)-cycle frame. TheOberwolfach problem OP(m1α1,m2α2,…,mtαt),raised by Ringel, asks the existence of a 2-factorization ofKn(whennis odd) orKn−I(whennis even), in which each 2-factor consists of exactlyαicycles of lengthmi,i=1,2,…,t.In this paper, we show that there exists a({4,6},λ)-cycle frame of(Km⊗In)(λ)if and only ifλn≡0(mod2),m≥3,(n,m)∉{(1,3),(2t+1,2s)∣t≥0,s≥2}. Further we show that there exists a({3,4},1)-cycle frame ofKm⊗Inif and only ifm≥3andn≡0(mod2).As a consequence, we solve OP(3a,4b),OP(3a,6b)and OP(5a,10b)with some restrictions ona,b∈N.
