论文标题
避免在均匀的超图路径和周期中的单色子路径
Avoiding monochromatic sub-paths in uniform hypergraph paths and cycles
论文作者
论文摘要
我们提出了一种递归公式，用于在$ j $ blue上涂上颜色的数量，以$ n $的r-均匀超速级为蓝色，同时避免使用长度为k的蓝色单色亚hyper。我们使用此结果来解决$（R-1）$ - 紧密的R-均匀路径和松动的R-均匀周期的相应问题。这概括了可靠性工程和分析的一些众所周知的结果。
We present a recursive formula for the number of ways to color $j$ vertices blue in an r-uniform hyperpath of size $n$ while avoiding a blue monochromatic sub-hyperpath of length k. We use this result to solve the corresponding problem for $(r-1)$-tight r-uniform paths and loose r-uniform cycles. This generalizes some well known results from reliability engineering and analysis.
