论文标题
加莱的猜想，以完成完整和“几乎完整”图
Gallai's Conjecture for Complete and "Nearly Complete" Graphs
论文作者
论文摘要
著名的加莱（Gallai）的猜想表明，与N顶点的任何连接图具有最多包含（n+1）/2路径的路径分解。在本说明中，我们探索了从完整图中删除边缘生成的图形。我们首先为满足Gallai猜想的完整图的路径分解提供了明确的结构。然后，我们使用该构造来证明我们可以去除恒星和某些t，以使所得图仍然满足加莱的猜想。我们还通过分析完整图的非同形路径分解来引入潜在的一般方法。
The famous Gallai's Conjecture states that any connected graph with n vertices has a path decomposition containing at most (n+1)/2 paths. In this note, we explore graphs generated from removing edges from complete graphs. We first provide an explicit construction for a path decomposition of complete graphs that satisfies Gallai's Conjecture. We then use that construction to prove that we can remove stars and certain tadpoles such that the resulting graph still satisfies Gallai's Conjecture. We also introduce a potential general approach through analyzing non-isomorphic path decompositions of complete graphs.
