  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 $\l\ge 2$ be an integer. The
current authors proved that a graph is 4- colorable if it has no cycles of
length less than $2\l+1$ and has no holes of odd length at least $2\l+3$.
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.
