不含平衡圈的符号图的分解
Decomposition of Signed Graphs without Contain Balanced Cycle
DOI: 10.12677/AAM.2023.124153, PDF,   
作者: 朱晨波：浙江师范大学数学科学学院，浙江 金华
关键词: 符号图；拟阵；图的分解；最大平均度；Signed Graphs； Matroids； Decomposition of Graphs； Maximum Average Degree
摘要: 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上的参数大于等于，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B1和I，且I在G中导出图G[I]中顶点最大度为d。
Abstract: 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 is greater than , then we prove when k=1 and any positive integers d, the signed graph G without con-tains any balanced cycle can decompose into two independent sets B1 and I, the degree of vertex in the induced graph G[I] is at most d.
文章引用：朱晨波. 不含平衡圈的符号图的分解[J]. 应用数学进展, 2023, 12(4): 1483-1486. https://doi.org/10.12677/AAM.2023.124153

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