A chromatic-index-critical graph $G$ on $n$ vertices is non-trivial if it has at most $\Delta \lfloor \frac{n}{2} \rfloor$ edges.
We prove that there is no chromatic-index-critical graph of order 12, and that there are precisely two non-trivial chromatic index critical graphs on 11 vertices.
Together with known results this implies that there are precisely
three non-trivial chromatic-index-critical graphs of order $\leq 12$.
Paper Available at:
ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1997/97-59.ps.gz
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