Graph Coloring · Hard problem

A hub vertex $0$ is the shared meeting point of THREE separate pentagons: arm $1$ is $0,1,2,3,4$, arm $2$ is $0,5,6,7,8$, and arm $3$ is $0,9,10,11,12$ ($13$ vertices, $15$ edges, the hub has degree $6$, and there is no triangle anywhere). This graph is connected, not complete, and not an odd cycle. What is its chromatic number?