Ubiquity of graphs with nowhere‐linear end structure
Ubiquity of graphs with nowhere‐linear end structure
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普遍存在非线性末端结构的图
DOI：
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发表时间：
2023
影响因子：
0.9
通讯作者：
Maximilian Teegen
中科院分区：
文献类型：
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作者：
N. Bowler;C. Elbracht;Joshua Erde;J. P. Gollin;K. Heuer;Max Pitz;Maximilian Teegen
图G$G$称为≼$precurlyeq$-泛在图，其中≼$precurlyeq$是图之间的次要关系，如果每当Γ${
M{Gamma}}$是一个图，其中Ng≼Γ$nGprcurlyeq{
对于所有n∈N$nin{mathbb{N}}$，M{Gamma}}$，则还有ℵ0g≼Γ${alph}_{0}gprocurlyeq{
M{GAMMA}}$，其中αG$αG$是α$α$多个副本G$G$的不交并。Andreae的一个著名猜想是，每个局部有限连通图都是≼$precurlyeq$-泛在图。本文给出了图G$G$的两端结构的一个充分条件，即图G$G$是≼$precurlyeq$-泛在图。特别是，这意味着全网格是无处不在的≼$precurlyeq$。
A graph G $G$ is said to be ≼ $preccurlyeq $ ‐ubiquitous, where ≼ $preccurlyeq $ is the minor relation between graphs, if whenever Γ ${
m{Gamma }}$ is a graph with nG≼Γ $nGpreccurlyeq {
m{Gamma }}$ for all n∈N $nin {mathbb{N}}$ , then one also has ℵ0G≼Γ ${aleph }_{0}Gpreccurlyeq {
m{Gamma }}$ , where αG $alpha G$ is the disjoint union of α $alpha $ many copies of G $G$ . A well‐known conjecture of Andreae is that every locally finite connected graph is ≼ $preccurlyeq $ ‐ubiquitous. In this paper we give a sufficient condition on the structure of the ends of a graph G $G$ which implies that G $G$ is ≼ $preccurlyeq $ ‐ubiquitous. In particular this implies that the full‐grid is ≼ $preccurlyeq $ ‐ubiquitous.