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 ...

hey climb walls and scuttle upside down across ceilings, dive to the ocean floor to feed on algae, even glide through the air from treetops. Some, with no limbs and extremely long tails, look like snakes; others are snakes. Many are nearly invisible in their home habitats; others announce their presence to their neighbors and warn off potential rivals by flashing colorful dewlaps, or fanlike st...