Partitioning Chordal Graphs

Obstructions to partitions of chordal graphs

“…On the other hand, when is near m (recall that k has to be at least two for the matrix to contain M 1 or M 2 ), the number of matrices with infinitely many chordal minimal obstructions is of the order of T 1− k, . For comparison, matrices with finitely many chordal minimal obstruc-tions include all matrices without * [10] or without 1 [14] or without 0 [14], so there are at least 3 · 2 ( m 2 ) such matrices for any k, . We do not know whether there are more matrices with finitely or with infinitely many chordal minimal obstructions.…”