2025/11/11 by Chengli Li, Li, Chengli, Xingzhi Zhan +1
Mathematics · Engineering · Computer Science · #Limits and Structures in Graph Theory #graph theory and CDMA systems #Advanced Graph Theory Research
paper · pdf · doi:10.48550/arxiv.2511.07758
A graph G is called an [s,t]-graph if any induced subgraph of G of order s has size at least t. An edge e in a graph G of order n is called pancyclic if for every integer k with 3≤ k≤ n, e lies in a k-cycle. We prove that every 2-connected [4, 2]-graph of order at least seven contains a pancyclic edge. This strengthens an existing result. We also determine the minimum size of a [4, 2]-graph of a given order and show that any [4, 2]-graph of order at least eight is not uniquely hamiltonian.