Edgewise strongly shellable clutters

When 𝒞 is a chordal clutter in the sense of Woodroofe or Emtander, we show that the complement clutter is edgewise strongly shellable. When 𝒞 is indeed a finite simple graph, we provide additional characterization of chordal graphs from the point of view of strong shellability. In particular, the generic graph GT of a tree is shown to be bi-strongly shellable.