Linear quotients of connected ideals of graphs

被引：0

作者：

Ananthnarayan, H. ^{[1
]}

Javadekar, Omkar ^{[1
]}

Maithani, Aryaman ^{[2
]}

机构：

[1] Indian Inst Technol, Dept Math, Mumbai 400076, Maharashtra, India

[2] Univ Utah, Dept Math, 155 South 1400 East, Salt Lake City, UT 84112 USA

来源：

JOURNAL OF ALGEBRAIC COMBINATORICS | 2025年 / 61卷 / 03期

关键词：

Independence complex; Stanley-Reisner ideal; Edge ideal; Linear resolution; Shellable; Linear quotients;

D O I：

10.1007/s10801-025-01395-6

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

As a higher analogue of the edge ideal of a graph, we study the t-connected ideal J(t). This is the monomial ideal generated by the connected subsets of size t. For chordal graphs, we show that J(t) has a linear resolution iff the graph is t-gap-free, and that this is equivalent to having linear quotients. We then show that if G is any gap-free and t-claw-free graph, then J(t)(G) has linear quotients and, hence, linear resolution.

引用

页数：15

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