@Article{Wang2025,
author = "Wang, Yanyan and Yang, Xiaojing",
title = "Local properties of graphs that induce global cycle properties",
journal = "Opuscula Math.",
year = "2025",
volume = "45",
number = "2",
pages = "275--285",
doi = "https://doi.org/10.7494/OpMath.2025.45.2.275",
url = "https://doi.org/10.7494/OpMath.2025.45.2.275",
abstract = "A graph \(G\) is locally Hamiltonian if \(G[N(v)]\) is Hamiltonian for every vertex \(v\in V(G)\). In this note, we prove that every locally Hamiltonian graph with maximum degree at least \(|V(G)| - 7\) is weakly pancyclic. Moreover, we show that any connected graph \(G\) with \(\Delta(G)\leq 7\) and \(\delta(G[N(v)])\geq 3\) for every \(v\in V (G)\), is fully cycle extendable. These findings improve some known results by Tang and Vumar.",
keywords = "fully cycle extendability, weakly pancyclicity, locally connected",
issn = "1232-9274"
}