论文标题
几乎所有9个常规图都具有模量-5取向
Almost all 9-regular graphs have a modulo-5 orientation
论文作者
论文摘要
1972年，图特（Tutte）著名地猜想，每个4边缘连接的图都没有一个零3流。已知这相当于每个5台式4边连接图的边缘方向，每个级别的每个级为1或4。受Pralat和Wormald的工作的启发，调查了$ P = 1 $，对于$ P = 2 $，我们表明这是渐近的，几乎肯定是随机的9台式图。因此，该猜想对几乎所有9个规范，8边缘连接的图都保留。这些结果利用了技术小仪调理方法。
In 1972 Tutte famously conjectured that every 4-edge-connected graph has a nowhere zero 3-flow; this is known to be equivalent to every 5-regular, 4-edge-connected graph having an edge orientation in which every in-degree is either 1 or 4. Jaeger conjectured a generalization of Tutte's conjecture, namely, that every $4p+1$-regular, $4p$-edge-connected graph has an edge orientation in which every in-degree is either $p$ or $3p+1$. Inspired by the work of Pralat and Wormald investigating $p=1$, for $p=2$ we show this holds asymptotically almost surely for random 9-regular graphs. It follows that the conjecture holds for almost all 9-regular, 8-edge-connected graphs. These results make use of the technical small subgraph conditioning method.
