Linear quotients of connected ideals of graphs

Abstract

As a higher analogue of the edge ideal of a graph, we study the $t$-connected ideal $J_t$. This is the monomial ideal generated by the connected subsets of size $t$. For chordal graphs, we show that $J_t$ has a linear resolution iff the tree is $t$-gap-free, and that this is equivalent to having linear quotients. We then show that if $G$ is any gap-free and $t$-claw-free graph, then $J_t(G)$ has linear quotients and, hence, linear resolution.

arXiv comment12 pages. This is the final version of the article, which has now appeared in the Journal of Algebraic Combinatorics

References in corpus (2)

• Results on the regularity of square-free monomial ideals
• Chordal graphs, higher independence and vertex decomposable complexes

Cited by in corpus (1)

• On the path ideals of chordal graphs