Grundy支配强积猜想的一个证明
组合数学
2023-01-16 v2
摘要
简单图G = (V,E)的Grundy支配数是指满足如下性质的最长唯一顶点序列S = (v_1, …, v_k)（v_i ∈ V）的长度：对每个i ∈ [k]，有N[v_i] \ ∪_{j=1}^{i-1}N[v_j] ≠ ∅。此处，N(v) = {u : uv ∈ E}，N[v] = N(v) ∪ {v}。在本注记中，我们证明了一个近期关于两个图强积的Grundy支配数的猜想。随后我们讨论了该结果如何与图的强积的零强迫数相关联。
引用
@article{arxiv.2212.04565,
title = {A Proof of the Grundy domination strong product conjecture},
author = {Rebekah Herrman and Stephen G. Z. Smith},
journal= {arXiv preprint arXiv:2212.04565},
year = {2023}
}
备注
There is an error. Some cases were not considered in the proof of Theorem 1