The minimum size of a $k$-connected locally nonforesty graph
Combinatorics
2025-01-27 v1
Abstract
A local subgraph of a graph is the subgraph induced by the neighborhood of a vertex. Thus a graph of order has local subgraphs. A graph is called locally nonforesty if every local subgraph of contains a cycle. Clearly, a graph is locally nonforesty if and only if every vertex of the graph is the hub of a wheel. We determine the minimum size of a -connected locally nonforesty graph of order
Keywords
Cite
@article{arxiv.2501.13980,
title = {The minimum size of a $k$-connected locally nonforesty graph},
author = {Chengli Li and Yurui Tang and Xingzhi Zhan},
journal= {arXiv preprint arXiv:2501.13980},
year = {2025}
}
Comments
12 pages, 2 figures. arXiv admin note: substantial text overlap with arXiv:2410.23702