The Erdos-Gyaras conjecture asserts that every graph with minimum degree at least three has a cycle whose length is a power of 2. Let G be a graph with minimum degree at least 3. We show that if G contains no induced path of order 10, then G contains a cycle of length 4 or 8, and hence the conjecture holds in this case. (c) 2024 Elsevier B.V. All rights are reserved, including those for text and d...
