Shellable graphs and sequentially Cohen-Macaulay bipartite graphs

Simple item page
dc.creatorVan Tuyl, Adam
dc.creatorVillarreal, Rafael H.
dc.date2007-01-10
dc.date2007-11-06
dc.date.accessioned2026-07-07T08:40:51Z
dc.date.available2026-07-07T08:40:51Z
dc.descriptionAssociated to a simple undirected graph G is a simplicial complex whose faces correspond to the independent sets of G. We call a graph G shellable if this simplicial complex is a shellable simplicial complex in the non-pure sense of Bjorner-Wachs. We are then interested in determining what families of graphs have the property that G is shellable. We show that all chordal graphs are shellable. Furthermore, we classify all the shellable bipartite graphs; they are precisely the sequentially Cohen-Macaulay bipartite graphs. We also give an recursive procedure to verify if a bipartite graph is shellable. Because shellable implies that the associated Stanley-Reisner ring is sequentially Cohen-Macaulay, our results complement and extend recent work on the problem of determining when the edge ideal of a graph is (sequentially) Cohen-Macaulay. We also give a new proof for a result of Faridi on the sequentially Cohen-Macaulayness of simplicial forests.
dc.description16 pages; more detail added to some proofs; Corollary 2.10 was been clarified; the beginning of Section 4 has been rewritten; references updated; to appear in J. Combin. Theory, Ser. A
dc.identifierhttps://arxiv.org/abs/math/0701296
dc.identifierhttp://arxiv.org/abs/math/0701296
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/141497
dc.subjectCombinatorics
dc.subjectCommutative Algebra
dc.subject13F55, 13D02, 05C38, 05C75
dc.titleShellable graphs and sequentially Cohen-Macaulay bipartite graphs
dc.typetext

Files

Collections

arXiv