Let x and y be two vertices lying on an oriented cycle in a connected valued translation quiver (Γ,τ,δ). We prove that, under certain conditions, x and y belong to the same cyclic component of (Γ,τ,δ) if and only if there is an oriented cycle in (Γ,τ,δ) passing through x and y.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm105-1-5,
author = {Piotr Malicki},
title = {On cyclic vertices in valued translation quivers},
journal = {Colloquium Mathematicae},
volume = {106},
year = {2006},
pages = {45-50},
zbl = {1096.16006},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm105-1-5}
}
Piotr Malicki. On cyclic vertices in valued translation quivers. Colloquium Mathematicae, Tome 106 (2006) pp. 45-50. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm105-1-5/