论文标题
3边缘可着色的立方签名图的流量
Flows of 3-edge-colorable cubic signed graphs
论文作者
论文摘要
Bouchet在1983年猜想，每个流动符号签名的图都允许一个零6流的零零6流，这等同于限制到立方签名的图。在本文中，我们证明了每个流动加速$ 3 $ - 可着色的立方签名图的图形都不是零零$ 10 $ - 流。这与4色定理一起意味着每个流动的无桥式平面签名图都允许零零$ 10 $ - 流。作为副产品，我们还表明，每个流动加热的哈密顿签名图都允许零零$ 8 $流。
Bouchet conjectured in 1983 that every flow-admissible signed graph admits a nowhere-zero 6-flow which is equivalent to the restriction to cubic signed graphs. In this paper, we proved that every flow-admissible $3$-edge-colorable cubic signed graph admits a nowhere-zero $10$-flow. This together with the 4-color theorem implies that every flow-admissible bridgeless planar signed graph admits a nowhere-zero $10$-flow. As a byproduct, we also show that every flow-admissible hamiltonian signed graph admits a nowhere-zero $8$-flow.
