On quasi-equigenerated and Freiman cover ideals of graphs

Drabkin, Benjamin; Guerrieri, Lorenzo

doi:10.1080/00927872.2020.1762890

Cited by 8 publications

(5 citation statements)

References 12 publications

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“…Behaviour of µ(I s ) was considered in some other articles, see for example [1,10,16,17]. Recently, Drabkin and Guerrieri [3] studied Freiman cover ideals. Given a cover ideal J(G), it is a demanding task to find the minimal generating set of J(G) s or µ(J(G) s ).…”

Section: Figure 2 Recursive Definition Of Rooted List Of P N−2mentioning

confidence: 99%

Rooted order on minimal generators of powers of some cover ideals

Erey¹

2021

Preprint

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We define a total order, which we call rooted order, on minimal generating set of J(P n ) s where J(P n ) is the cover ideal of a path graph on n vertices. We show that each power of a cover ideal of a path has linear quotients with respect to the rooted order. Along the way, we characterize minimal generating set of J(P n ) s for s ≥ 3 in terms of minimal generating set of J(P n ) 2 . We also discuss the extension of the concept of rooted order to chordal graphs. Computational examples suggest that such order gives linear quotients for powers of cover ideals of chordal graphs as well.

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Section: Figure 2 Recursive Definition Of Rooted List Of P N−2mentioning

confidence: 99%

Rooted order on minimal generators of powers of some cover ideals

Erey¹

2021

Preprint

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“…This is a very restrictive condition for ideals arising from combinatorial structures, which often guarantees strong combinatorial properties. Many classes of Freiman ideals such as Hibi ideals, Veronese type ideals, matroid ideals, sortable ideals, principal Borel ideals, t-spread principal Borel ideals, edge ideals and cut ideals of several graphs, and cover ideals of some classes of graphs such as trees, circulant graphs, whiskered graphs and simple connected unmixed bipartite graphs have been studied (see [6,14,15,16,17,18]).…”

Section: Introductionmentioning

confidence: 99%

Freiman Borel type ideals

Zhu¹,

Zhao²,

Duan³

et al. 2022

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“…Freiman ideals in the classes of Hibi ideals, Veronese type ideals, matroid ideals, sortable ideals, edge ideals of several graphs, cover ideals of simple connected unmixed bipartite graphs, and cover ideals of some classes of graphs such as trees, circulant graphs, and whiskered graphs have been studied (see [3,8,10,11,13]).…”

Section: Introductionmentioning

confidence: 99%