Let G be a plane graph with exactly one triangle T and all other cycles oflength at least 5, and let C be a facial cycle of G of length at most six. Weprove that a 3-coloring of C does not extend to a 3-coloring of G if and onlyif C has length exactly six and there is a color x such that either G has anedge joining two vertices of C colored x, or T is disjoint from C and everyvertex of T is adjacent to a vertex of C colored x. This is a lemma to be usedin a future paper of this series.
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