We show that the second power of the cover ideal of a path graph has linear quotients.To prove our result we construct a recursively defined order on the generators of the ideal which yields linear quotients.Our const...We show that the second power of the cover ideal of a path graph has linear quotients.To prove our result we construct a recursively defined order on the generators of the ideal which yields linear quotients.Our construction has a natural generalization to the larger class of chordal graphs.This generalization allows us to raise some questions that are related to some open problems about powers of cover ideals of chordal graphs.展开更多
文摘We show that the second power of the cover ideal of a path graph has linear quotients.To prove our result we construct a recursively defined order on the generators of the ideal which yields linear quotients.Our construction has a natural generalization to the larger class of chordal graphs.This generalization allows us to raise some questions that are related to some open problems about powers of cover ideals of chordal graphs.
