Geodesic
Criterion for the existence of such a cycle that vertices beyond this cycle are independent
Zapiski Nauchnykh Seminarov POMI, Combinatorics and graph theory. Part XII, Tome 497 (2020), pp. 53-79 
N. A. Karol'. Criterion for the existence of such a cycle that vertices beyond this cycle are independent. Zapiski Nauchnykh Seminarov POMI, Combinatorics and graph theory. Part XII, Tome 497 (2020), pp. 53-79. http://geodesic.mathdoc.fr/item/ZNSL_2020_497_a2/
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     title = {Criterion for the existence of such a cycle that vertices beyond this cycle are independent},
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     url = {http://geodesic.mathdoc.fr/item/ZNSL_2020_497_a2/}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

This paper contains a criterion for the existence of such a cycle that the vertices beyond this cycle are independent in terms of minimum vertex degree. More specifically, if $G$ is a $2$-connected graph, $v(G) = n$ and $\delta(G) \geq \frac{n + 2}{3}$, then $G$ has a cycle such that vertices beyond this cycle are independent.

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