Nowhere-zero 3-flow of graphs with small independence number
Nowhere-zero 3-flow of graphs with small independence number
复制标题
DOI：
10.1016/j.disc.2017.06.022
复制
发表时间：
2017-07
期刊：
影响因子：
--
通讯作者：
Jiaao Li;Rong Luo;Yi Wang
中科院分区：
文献类型：
--
作者：
Jiaao Li;Rong Luo;Yi Wang
Tutte的3-流猜想指出，每个4-边连通图允许一个无处为零的3-流。本文刻画了所有独立数不超过4且允许非零3-流的图。3-流的刻画验证了Tutte关于独立数不超过4且阶数不小于21的图的3-流猜想。此外，我们还证明了每一个独立数不超过3的奇5边连通图都有一个无处为零的3流。为了得到这些结果，我们引入了一个新的减少方法来处理奇数轮。
Tutte’s 3-flow conjecture states that every 4-edge-connected graph admits a nowhere-zero 3-flow. In this paper, we characterize all graphs with independence number at most 4 that admit a nowhere-zero 3-flow. The characterization of 3-flow verifies Tutte’s 3-flow conjecture for graphs with independence number at most 4 and with order at least 21. In addition, we prove that every odd-5-edge-connected graph with independence number at most 3 admits a nowhere-zero 3-flow. To obtain these results, we introduce a new reduction method to handle odd wheels.