Worpitzky-compatible subarrangements of braid arrangements and cocomparability graphs

The class of Worpitzky-compatible subarrangements a Weyl arrangement together with an associated Eulerian polynomial was recently introduced by Ashraf, Yoshinaga and the first author, which brings characteristic Ehrhart quasi-polynomials into one formula. braid arrangement, type A, are known as graphic arrangements. We prove that arrangements characterized cocomparability graphs. This can be regarded counterpart characterization Stanley Edelman–Reiner free supersolvable in terms chordal Our main result yields new formulas for chromatic polynomials