Linear Balanceable and Subcubic Balanceable Graphs*
Linear Balanceable and Subcubic Balanceable Graphs*
复制标题
线性平衡图和次三次平衡图*
DOI：
10.1002/jgt.21728
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发表时间：
2013
影响因子：
0.9
通讯作者：
Aboulker P
中科院分区：
文献类型：
--
作者：
Aboulker P
Conforti和Rao在Math Program 55(1992)，129-168中猜想，每个平衡二部图都包含一条不是圈的唯一弦的边。对于不含4圈的平衡二部图(也称为线性平衡二部图)，以及最大度不超过3的平衡二部图，我们证明了这一猜想。事实上，我们得到了更一般类的结果，即线性可平衡图和次三次可平衡图。此外，我们还证明了三次平衡图包含一对孪生组织，这是Morris，Spiga和Webb在(离散数学310(2010)，3228-3235)中猜想的结果。
In Math Program 55(1992), 129–168, Conforti and Rao conjectured that every balanced bipartite graph contains an edge that is not the unique chord of a cycle. We prove this conjecture for balanced bipartite graphs that do not contain a cycle of length 4 (also known as linear balanced bipartite graphs), and for balanced bipartite graphs whose maximum degree is at most 3. We in fact obtain results for more general classes, namely linear balanceable and subcubic balanceable graphs. Additionally, we prove that cubic balanced graphs contain a pair of twins, a result that was conjectured by Morris, Spiga, and Webb in ( Discrete Math 310(2010), 3228–3235).