Ideal subarrangements of a Weyl arrangement are proved to be free by the
multiple addition theorem (MAT) due to Abe-Barakat-Cuntz-Hoge-Terao (2016).
They form a significant class among Weyl subarrangements that are known to be
free so far. The concept of MAT-free arrangements was introduced recently by
Cuntz-M{\"u}cksch (2020) to capture a core of the MAT, which enlarges the ideal
subarrangements from the perspective of freeness. The aim of this paper is to
give a precise characterization of the MAT-freeness in the case of type A
Weyl subarrangements (or graphic arrangements). It is known that the ideal and
free graphic arrangements correspond to the unit interval and chordal graphs
respectively. We prove that a graphic arrangement is MAT-free if and only if
the underlying graph is strongly chordal. In particular, it affirmatively
answers a question of Cuntz-M{\"u}cksch that MAT-freeness is closed under
taking localization in the case of graphic arrangements.Comment: 25 page
