3- and 4-critical graphs of small even order

G. Brinkmann, E. Steffen
1997 Discrete Mathematics  
We show that there is exactly one 3-critical graph of order 22 and that there are exactly nine of order 24. The graph of order 22 is shown to be the smallest 3-critical graph of even order. We also show that there are exactly two 4-critical graphs of order 18, and that these graphs are the smallest 4-critical graphs of even order. The results are obtained with the aid of a computer.
doi:10.1016/s0012-365x(96)00105-7 fatcat:sb2jte6nerbcto4pzs3m7c4lbi