%0 Journal Article
%T 不含平衡圈的符号图的分解<br>Decomposition of Signed Graphs without Contain Balanced Cycle
%A 朱晨波
%J Advances in Applied Mathematics
%P 1483-1486
%@ 2324-8009
%D 2023
%I Hans Publishing
%R 10.12677/AAM.2023.124153
%X 本文主要在符号图框架拟阵的定义下，通过证明所含的圈中没有平衡圈的符号图G上的参数<img src=\"Edit_1ae8ad4d-c446-4bb4-90bf-cc7dd622727c.png\" alt=\"\" />大于等于<img src=\"Edit_dc172aa0-65c4-4de8-b4c8-d745e097cc7c.png\" alt=\"\" />，从而证明在k=1，以及任意的非负整数d的条件下，不含平衡圈的符号图能分解成两个独立集B<sub>1</sub>和I，且I在G中导出图G[I]中顶点最大度为d。<br />
In this paper, we study the signed graph based on the frame matroid. For the signed graph G with-out contains any balanced cycle, we prove the parameter <img src=\"Edit_74d7ab52-e951-4650-8d31-0d13891be38c.png\" alt=\"\" /> is greater than <img src=\"Edit_f53c9acf-9b54-41cf-839a-4ddf987ed639.png\" alt=\"\" /> , then we prove when <span>k=1</span> and any positive integers d, the signed graph G without con-tains any balanced cycle can decompose into two independent sets <span>B</span><sub>1</sub> and I, the degree of vertex in the induced graph <span>G[I]</span> is at most d.
%K 符号图，拟阵，图的分解，最大平均度<br>Signed Graphs
%K Matroids
%K Decomposition of Graphs
%K Maximum Average Degree
%U http://www.hanspub.org/journal/PaperInformation.aspx?PaperID=64072