2019/08/28 by Selvaraja, S
#13F20 #Combinatorics (math.CO) #Commutative Algebra (math.AC) #FOS: Mathematics #primary: 13D02
paper · doi:10.48550/arxiv.1908.10576
Let G be a finite simple graph and J(G) denote its cover ideal in a polynomial ring over a field \mathbbK. In this paper, we show that all symbolic powers of cover ideals of certain vertex decomposable graphs have linear quotients. Using these results, we give various conditions on a subset S of the vertices of G so that all symbolic powers of vertex cover ideals of G ∪ W(S), obtained from G by adding a whisker to each vertex in S, have linear quotients. For instance, if S is a vertex cover of G, then all symbolic powers of J(G ∪ W(S)) have linear quotients. Moreover, we compute the Castelnuovo-Mumford regularity of symbolic powers of certain cover ideals.