Your list of 4 regular 4 chromatic graphs with girth >= 4 is not complete. Check "A note on 4-regular 4 chromatic graphs with girth 4" http://math.nju.edu.cn/~zkmfl/kmzhang/41-60/Zhang44.pdf. Girth 5 is known too.

## The list of known graphs is not full

Your list of 4 regular 4 chromatic graphs with girth >= 4 is not complete. Check "A note on 4-regular 4 chromatic graphs with girth 4" http://math.nju.edu.cn/~zkmfl/kmzhang/41-60/Zhang44.pdf. Girth 5 is known too.