Chromatic-Index-Critical Graphs of Orders 11 and 12

A chromatic-index-critical graphGonnvertices is non-trivial if it has at most Δ ⌊n2⌋ 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 ≤12.