What question did this study set out to answer?

To establish conditions for the vertex decomposability of clique complexes associated with simple graphs.

A Class of Vertex Decomposable Flag Simplicial Complexes

View Full Paper

Ask AI

Bookmark

To establish conditions for the vertex decomposability of clique complexes associated with simple graphs.
Investigated the structural characterization of vertex decomposable ligand simplicial complexes.
Proved the relationship between induced subgraphs and vertex decomposability of the clique complex CL(G).
Utilized properties of chordal graphs and their independence complexes.
Confirmed that CL(G) is vertex decomposable if G contains no induced subgraphs isomorphic to 2K2, C4, or C5.
Demonstrated that all vertex decomposable complexes are shellable and partitionable.
Established implications for Stanley’s conjecture regarding the face ring K[CL(G)].

No takes yet. Share an insight, caveat, or question.

The analysis uncovers induced subgraphs in simple graphs, suggesting new insights into vertex decomposable complexes.

A 2025 study studied this question.

View Full Paper

Ask AI

Bookmark