Claims

../

1988_01_01_erdos_faudree_gyarfas_schelp: Theorem 2 of Erdős, Faudree, Gyárfás and Schelp (Ars Combin. 25B, 1988) gives a triangle and a 5-cycle in every graph of the class on at least 5 vertices and a 4-cycle on at least 6; the cases k = 3, 4, 5 of the problem.

2014_08_22_narins_pokrovskiy_szabo: Narins, Pokrovskiy and Szabó (Combinatorica 2017) build arbitrarily large graphs with n vertices, 2n - 2 edges, no proper induced subgraph of minimum degree 3 and no 23-cycle; refereed and credited by the site's curator.

---