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The graphs with Hall number at most 2 form a class of graphs within which the chromatic number equals the choice (list-chromatic) number. This class has a forbidden-induced-subgraph characterization which has not yet been found, although a fairly imposing collection of minimal forbidden induced subgraphs has been assembled. In this paper
we add to the collection, most notably adding
(i) $K_5$ with an ear of length 2 attached;
(ii) $K_4$ with an ear of any length $>2$ attached;
(iii) any cycle together with two triangles based on incident edges on the cycle;
(iv) any odd cycle together with two triangles based on non-incident edges
of the cycle; and
(v) any even cycle together with three triangles based on non-incident edges of the cycle.
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