# Chromatic-Index-Critical Graphs of Orders 11 and 12

```@article{Brinkmann1998ChromaticIndexCriticalGO,
title={Chromatic-Index-Critical Graphs of Orders 11 and 12},
author={Gunnar Brinkmann and Eckhard Steffen},
journal={Eur. J. Comb.},
year={1998},
volume={19},
pages={889-900}
}```
• Published 1 November 1998
• Mathematics
• Eur. J. Comb.
Abstract A chromatic-index-critical graphGonnvertices is non-trivial if it has at most Δ ⌊ n 2 ⌋ 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.
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