论文标题
含色的音量
The chromatic number of heptagraphs
论文作者
论文摘要
一个孔是一个至少4个长度的诱导循环。如果它没有长度为3或4的循环，则将图称为Pentagraph，并且没有奇数长度至少7个孔，如果没有长度小于7的循环，并且没有奇数长度的孔，则将其称为hptagraph，至少没有奇数长度为9。令$ \ ge 2 $。目前的作者证明，如果没有长度的循环小于$ 2万+1 $，并且没有奇数长度至少$2ł+3 $，则图表可着色。 Chudnovsky和Seymour证实了Plummer和Zha的猜想，证明了每个Pentagraph都是3色。遵循他们的想法，我们证明每枚Heptagh都是3色。
A hole is an induced cycle of length at least 4. A graph is called a pentagraph if it has no cycles of length 3 or 4 and has no holes of odd length at least 7, and is called a heptagraph if it has no cycles of length less than 7 and has no holes of odd length at least 9. Let $ł\ge 2$ be an integer. The current authors proved that a graph is 4- colorable if it has no cycles of length less than $2ł+1$ and has no holes of odd length at least $2ł+3$. Confirming a conjecture of Plummer and Zha, Chudnovsky and Seymour proved that every pentagraph is 3-colorable. Following their idea, we show that every heptagraph is 3-colorable.
