Chromatic-index-critical graphs of orders 13 and 14

In this paper we show that there are no chromatic-index-critical graphs of order 14. Our result extends that of [[5] G. Brinkmann, E. Steffen, Chromatic-index-critical graphs of orders 11 and 12, European J. Combin. 19 (1998) 889-900] and leaves order 16 as the only case to be checked in order to decide on the minimality of the counterexamples given by Chetwynd and Fiol. In addition we list all nontrivial critical graphs of order 13.