Let G be a triangle-free graph with δ(G) ≥ 2 and σ₄(G) ≥ |V(G)| + 2. Let S ⊂ V(G) consist of less than σ₄/4+ 1 vertices. We prove the following. If all vertices of S have degree at least three, then there exists a cycle C containing S. Both the upper bound on |S| and the lower bound on σ₄ are best possible.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1354,
author = {Daniel Paulusma and Kiyoshi Yoshimoto},
title = {Cycles through specified vertices in triangle-free graphs},
journal = {Discussiones Mathematicae Graph Theory},
volume = {27},
year = {2007},
pages = {179-191},
zbl = {1134.05043},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1354}
}
Daniel Paulusma; Kiyoshi Yoshimoto. Cycles through specified vertices in triangle-free graphs. Discussiones Mathematicae Graph Theory, Tome 27 (2007) pp. 179-191. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1354/
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