关于笼子猜想的证明
组合数学
2024-10-10 v1
摘要
图的周长定义为图中最短环的长度。在所有k正则且周长为g的图中顺序最小的图称为(k;g)-笼子。在图G中，若图G-V(C)保持连通，则环C称为非分离环。一个猜想于[T. Jiang, D. Mubayi. Connectivity and Separating Sets of Cages. J. Graph Theory 29(1)(1998) 35--44]提出，认为在(k;g)-笼子中，长度为g的每个环都是非分离的。虽然该猜想在上述工作中已证明偶数g的情况，但本文证明了该猜想对奇数g也成立。因此，先前的猜想已被证明为正确。
引用
@article{arxiv.2410.07028,
title = {The proof of a conjecture about cages},
author = {Xiang-Feng Pan and Jing-Zhong Mao and Hui-Qing Liu},
journal= {arXiv preprint arXiv:2410.07028},
year = {2024}
}
备注
This paper was published in Chinese on April 25, 2001, in Volume 14, Issue 2 of the "MATHEMATICA APPLICATA" on pages 99 to 102. This is the English version of the paper, incorporating additional details and rectifying certain typographical errors