无射线图的强纳什-威廉斯定向定理

arXiv - MATH - Combinatorics Pub Date : 2024-09-16 DOI:arxiv-2409.10378

Max Pitz, Jacob Stegemann

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引用次数: 0

摘要

1960 年，纳什-威廉斯证明了他的强定向定理，即每个无限图都有一个定向，其中任何两个顶点之间的有向路径数至少是它们之间无向路径数的一半（四舍五入）。纳什-威廉姆斯猜想，无限图也有可能找到这样的定向。通过证明所有无射线图都有这样的方向，我们给出了部分答案。

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The strong Nash-Williams orientation theorem for rayless graphs

In 1960, Nash-Williams proved his strong orientation theorem that every finite graph has an orientation in which the number of directed paths between any two vertices is at least half the number of undirected paths between them (rounded down). Nash-Williams conjectured that it is possible to find such orientations for infinite graphs as well. We provide a partial answer by proving that all rayless graphs have such an orientation.

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arXiv - MATH - Combinatorics

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