发表机构
Université Bourgogne Europe（勃艮第欧洲大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文通过超图全色与双全色着色，研究弦图中完全独立生成树的存在性，推翻一个相关猜想，并给出结构条件。
AI 中文摘要
本文通过适当的超图表示及其全色和双全色着色，研究弦图中完全独立生成树（CIST）的存在性问题。首先，我们推翻了一个猜想，该猜想声称超图的最优全色着色中，全色数、双全色数与唯一颜色最小数目之间存在精确关系。然后，通过将CIST与相关超图的全色和双全色着色联系起来，我们推导出它们在弦图以及严格弦图中存在的结构条件。
英文摘要
In this paper, we study the existence problem of completely independent spanning trees (CIST) in chordal graphs through appropriate hypergraph representations and their panchromatic and bipanchromatic colorings. First, we disprove a conjecture stating an exact relationship between the panchromatic number, the bipanchromatic number, and the minimum number of unique colors in an optimal panchromatic coloring of a hypergraph. Then, by relating CIST to panchromatic and bipanchromatic colorings of the associated hypergraphs, we derive structural conditions for their existence in chordal graphs and specifically strictly chordal graphs.
Comments11 pages, 4 figures
