论文标题
Plummer和Zha的猜想的证明
Proof of a conjecture of Plummer and Zha
论文作者
论文摘要
假设图$ g $是一个{\ em pentagraph}，如果每个周期的长度至少五个，则每个奇数长度的诱发周期的长度为五。 N. Robertson提出了一个猜想，即Petersen图是唯一一个三连接且内部四连接的五角星，但这在2014年被M. Plummer和X. Zha所拒绝。Plummer和Zha指出，每一个内部的3个连接，内部4个连接的五角形都是三色的。我们证明了这一点：的确，我们将证明每个五角星都是三色。
Say a graph $G$ is a {\em pentagraph} if every cycle has length at least five, and every induced cycle of odd length has length five. N. Robertson proposed the conjecture that the Petersen graph is the only pentagraph that is three-connected and internally 4-connected, but this was disproved by M. Plummer and X. Zha in 2014. Plummer and Zha conjectured that every 3-connected, internally 4-connected pentagraph is three-colourable. We prove this: indeed, we will prove that every pentagraph is three-colourable.
