1. Symbolic powers of vertex cover ideals
- Author
-
S. Selvaraja
- Subjects
Discrete mathematics ,Ideal (set theory) ,Simple graph ,Mathematics::Commutative Algebra ,Computer Science::Information Retrieval ,General Mathematics ,Polynomial ring ,Astrophysics::Instrumentation and Methods for Astrophysics ,Vertex cover ,Computer Science::Computation and Language (Computational Linguistics and Natural Language and Speech Processing) ,Field (mathematics) ,primary: 13D02, 13F20 ,Mathematics - Commutative Algebra ,Commutative Algebra (math.AC) ,TheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGES ,FOS: Mathematics ,Mathematics - Combinatorics ,Computer Science::General Literature ,Combinatorics (math.CO) ,Symbolic power ,ComputingMilieux_MISCELLANEOUS ,MathematicsofComputing_DISCRETEMATHEMATICS ,Mathematics - Abstract
Let $G$ be a finite simple graph and $J(G)$ denote its cover ideal in a polynomial ring over a field $\mathbb{K}$. 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 $G \cup W(S)$, 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 $J(G \cup W(S))$ have linear quotients. Moreover, we compute the Castelnuovo-Mumford regularity of symbolic powers of certain cover ideals., Comment: 15 pages, 2 figures
- Published
- 2020