Cohen-Macaulay graphs with large girth

Abstract

We classify Cohen-Macaulay graphs of girth at least $5$ and planar Gorenstein graphs of girth at least $4$. Moreover, such graphs are also vertex decomposable.

14 pages, to appear in JAA. This is a revised version of http://arxiv.org/abs/1204.5561

References in corpus (2)

• Vertex decomposable graphs and obstructions to shellability
• Equality of ordinary and symbolic powers of Stanley-Reisner ideals

Cited by in corpus (1)

• Vertex decomposable graphs, codismantlability, Cohen-Macaulayness and Castelnuovo-Mumford regularity