An extension of an induced path P in a graph G is ′ such that deleting the endpoints results P. said to be avoidable if each its extensions contained cycle. In 2019, Beisegel, Chudovsky, Gurvich, Milanič, and Servatius conjectured every contains k-vertex also same length, proved result for k = 2. The case 1 was known much earlier, due work Ohtsuki, Cheung, Fujisawa 1976. conjecture all 2020 by ...