%0 Journal Article
%T 关于双树度差下界的一个例子<br>An Example of the Bound of Double Tree
%A 张雅琴
%J Advances in Applied Mathematics
%P 1615-1619
%@ 2324-8009
%D 2023
%I Hans Publishing
%R 10.12677/AAM.2023.124166
%X 如果图G由两个边不交的生成树的并组成，其中E(G)=E(T<sub>1</sub>)∪E(T<sub>2</sub>)，且E(T<sub>1</sub>)∩E(T<sub>2</sub>)=？那么称图G是双树。本文证明存在一个双树G，对于G任意一个分解f=<span>T</span><sub>1</sub>,T<sub>2</sub>而言(<span>T</span><sub>1</sub><span>,</span><span>T</span><sub>2</sub>是生成树)，至少存在一个顶点v∈V(G)，使得▏d<sub>T1</sub>(v)-d<sub>T2</sub>(v)▏≥2。<br />
If the graph G contains two spanning trees such that the edges of spanning trees are disjoint. And <span>E(G)=E(T</span><sub>1</sub><span>)∪E(T</span><sub>2</sub><span>)</span> and <span>E(T</span><sub>1</sub><span>)∩E(T</span><sub>2</sub><span>)=？</span> , then we call the graph G is double tree. In this pa-per we prove that there exists a double tree graph G, for any decomposition <span>f=</span><span>T</span><sub>1</sub><span>,T</span><sub>2</sub> (<span>T</span><sub>1</sub><span>,</span><span>T</span><sub>2</sub> are spanning trees), there exists at least a vertex <span>v∈V(G)</span> such that <span>▏d</span><sub>T1</sub><span>(v)-d</span><sub>T2</sub><span>(v)▏≥2</span> .
%K 双树，分解，生成树<br>Double Tree
%K Decomposition
%K Spanning Tree
%U http://www.hanspub.org/journal/PaperInformation.aspx?PaperID=64524