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The moduli stack of Deligne-Mumford stable curves of genus g admits astratification, so that the number of nodes of the curves belonging to onestratum is constant. The irreducible components of the stratum corresponding tocurves with exactly 3g-4 nodes are one-dimensional substacks. We show how theycan be related to moduli stacks of (permutation classes of) pointed stablecurves. Using this, we construct all components of this stratum in a new way asquotient stacks.

The one-dimensional stratum in the boundary of the moduli stack of stable curves