Erd\H{o}s-Gy\'{a}rf\'{a}s Conjecture for $P_8$-free graphs
Combinatorics
2021-09-06 v1
Abstract
A graph is -free if it contains no induced subgraph isomorphic to the path on eight vertices. In 1995, Erd\H{o}s and Gy\'{a}rf\'{a}s conjectured that every graph of minimum degree at least three contains a cycle whose length is a power of two. In this paper, we confirm the conjecture for -free graphs by showing that there exists a cycle of length four or eight in every -free graph with minimum degree at least three.
Cite
@article{arxiv.2109.01277,
title = {Erd\H{o}s-Gy\'{a}rf\'{a}s Conjecture for $P_8$-free graphs},
author = {Yuping Gao and Songling Shan},
journal= {arXiv preprint arXiv:2109.01277},
year = {2021}
}
Comments
10pages