… on the edge ideal of a graph G, we study the equivalent … of vertex decomposability from
geometric combinatorics, we show that 5chordal graphs with no chordless 4-cycles are shellable …

… shellable and vertex decomposable graphs. In Theorem 2.5, we show that for a shellable
graph … G) and in Corollary 2.9 it is shown that for a vertex decomposable graph G, reg(R/I(G)) ≤ …

… shellable, R/I∆ is Cohen-Macaulay, G is unmixed vertex … vertex decomposable graphs
without 3-cycles and 5-cycles. This result generalize the criterion given in [19] for shellable graphs. …

… A graph G is called vertex decomposable or shellable if Ind(G) has this property. In [8] … the
notion of vertex decomposable for graphs as follows: A graph G is vertex decomposable if it is …

… vertices, then the notions of shellable, vertex decomposable, shelling completable, and
extendably … between shellable complexes and the notion of a chordal graph. Recall that a simple …

… study the minimal free resolution of vertex cover ideal of vertex decomposable graphs. The
paper is … implies the known fact that any vertex decomposable simplicial complex is shellable. …

… As in [20], we call a graph G a shellable graph if ∆(G) is a shellable simplicial complex. A
vertex decomposable graph is then shellable because of the following more general result (see …

… shellability of such combinatorially defined simplicial complexes. We establish a relation
between vertex decomposability and the CL-shellability … of general bipartite graphs). Following […

… shellable when the underlying chordal graph is a tree. Using the notion of vertex splittable
ideals we show that for caterpillar graphs … complex is vertex decomposable for all values of r. …

… We call a graph G vertex decomposable (resp. shellable, semi-nonevasive etc.) if the …
But we know by Theorem 3.2 that if G is a shellable very well-covered graph, then G is semi-…