On the strong persistence property and normality of cover ideals of theta graphs

Abstract

In this paper, we show that the cover ideals of theta graphs are normal square-free monomial ideals, and also satisfy the strong persistence property. Moreover, we re-prove a well-known result which is related to the cover ideals of bipartite graphs. We finally terminate this paper by stating some theorems which introduce some classes of normal monomial ideals.

Keywords:

• Imperfect graphs
• normal ideals
• strong persistence property
• theta graphs

2020 MATHEMATICS SUBJECT CLASSIFICATION:

• 13B25
• 13B22
• 13F20
• 05C25
• 05E40

Acknowledgments

The authors are deeply grateful to the referee for carefully reading of the manuscript.