Computational and Theoretical Challenges for Computing the Minimum Rank of a Graph

被引：3

作者：

Hicks, Illya, V ^{[1
]}

Brimkov, Boris ^{[2
]}

Deaett, Louis ^{[3
]}

Haas, Ruth ^{[4
]}

Mikesell, Derek ^{[1
]}

Roberson, David ^{[5
,6
]}

Smith, Logan ^{[1
]}

机构：

[1] Rice Univ, Computat Appl Math & Operat Res Dept, Houston, TX 77005 USA

[2] Slippery Rock Univ, Math & Stat Dept, Slippery Rock, PA 16057 USA

[3] Quninnipiac Univ, Math & Stat Dept, Hamden, CT 06518 USA

[4] Univ Hawaii Monoa, Dept Math, Honolulu, HI 96822 USA

[5] Tech Univ Denmark, Dept Appl Math & Comp Sci, DK-2800 Lyngby, Denmark

[6] Univ Copenhagen, Ctr Math Quantum Theory QMATH, Dept Math Sci, DK-2100 Copenhagen, Denmark

来源：

INFORMS JOURNAL ON COMPUTING | 2022年 / 34卷 / 06期

基金：

美国国家科学基金会;

关键词：

minimum rank; maximum nullity; matroid; zero forcing; forts; ZERO FORCING SETS; PATH COVER NUMBER; MAXIMUM NULLITY; PARAMETERS;

D O I：

10.1287/ijoc.2022.1219

中图分类号：

TP39 [计算机的应用];

学科分类号：

081203 ; 0835 ;

摘要：

The minimum rank of a graph G is the minimum of the ranks of all symmetric adjacency matrices of G. We present a new combinatorial bound for the minimum rank of an arbitrary graph G based on enumerating certain subsets of vertices of G satisfying matroid theoretic properties. We also present some computational and theoretical challenges associated with computing the minimum rank. This includes a conjecture that this bound on the minimum rank actually holds with equality for all graphs.

引用

页码：2868 / 2872

页数：5

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