On a rainbow version of Dirac's theorem

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For a collection G={G1,MIDLINE HORIZONTAL ELLIPSIS,Gs} of not necessarily distinct graphs on the same vertex set V, a graph H with vertices in V is a G-transversal if there exists a bijection phi:E(H)->[s] such that e is an element of E(G phi(e)) for all e is an element of E(H). We prove that for |V|=s > 3 and delta(Gi)> s/2 for each i is an element of[s], there exists a G-transversal that is a Hamilton cycle. This confirms a conjecture of Aharoni. We also prove an analogous result for perfect matchings.
Publisher
WILEY
Issue Date
2020-06
Language
English
Article Type
Article
Citation

BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, v.52, no.3, pp.498 - 504

ISSN
0024-6093
DOI
10.1112/blms.12343
URI
http://hdl.handle.net/10203/279378
Appears in Collection
MA-Journal Papers(저널논문)
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