19 research outputs found
Vertex decomposable graphs, codismantlability, Cohen-Macaulayness and Castelnuovo-Mumford regularity
We call a (simple) graph G codismantlable if either it has no edges or else
it has a codominated vertex x, meaning that the closed neighborhood of x
contains that of one of its neighbor, such that G-x codismantlable. We prove
that if G is well-covered and it lacks induced cycles of length four, five and
seven, than the vertex decomposability, codismantlability and
Cohen-Macaulayness for G are all equivalent. The rest deals with the
computation of Castelnuovo-Mumford regularity of codismantlable graphs. Note
that our approach complements and unifies many of the earlier results on
bipartite, chordal and very well-covered graphs
Regularity of squarefree monomial ideals
We survey a number of recent studies of the Castelnuovo-Mumford regularity of
squarefree monomial ideals. Our focus is on bounds and exact values for the
regularity in terms of combinatorial data from associated simplicial complexes
and/or hypergraphs.Comment: 23 pages; survey paper; minor changes in V.
Regularity of Edge Ideals and Their Powers
We survey recent studies on the Castelnuovo-Mumford regularity of edge ideals
of graphs and their powers. Our focus is on bounds and exact values of and the asymptotic linear function , for in terms of combinatorial data of the given graph Comment: 31 pages, 15 figure
The operation and operation of Cohen-Macaulay bipartite graphs
Let be a finite simple graph with the vertex set and let be its
edge ideal in the polynomial ring . In this paper, we
compute the depth and the Castelnuovo--Mumford regularity of when
or is a graph obtained from Cohen-Macaulay
bipartite graphs , by operation or operation,
respectively.Comment: arXiv admin note: text overlap with arXiv:2308.0601