论文标题
独立的覆盖物和正交颜色
Independent Coverings and Orthogonal Colourings
论文作者
论文摘要
在本文中，两个开放式猜想被反驳。一个猜想对稀疏部分图的独立覆盖物进行了介绍，而另一个猜想则为树图的正交着色。建立了独立覆盖物与正交着色之间的关系。该关系应用于找到一些稀疏党图的独立覆盖物。此外，在图形具有平方数量的顶点的情况下，提供独立覆盖的度条件。
In this paper, two open conjectures are disproved. One conjecture regards independent coverings of sparse partite graphs, whereas the other conjecture regards orthogonal colourings of tree graphs. A relation between independent coverings and orthogonal colourings is established. This relation is applied to find independent coverings of some sparse partite graphs. Additionally, a degree condition providing the existence of an independent covering in the case where the graph has a square number of vertices is found.
