THE ZERO FORCING NUMBER OF GRAPHS

被引：25

作者：

Kalinowski, Thomas ^{[1
]}

Kamcev, Nina ^{[2
]}

Sudakov, Benny ^{[2
]}

机构：

[1] Univ New England, Sch Sci & Technol, Armidale, NSW 2351, Australia

[2] ETH, Dept Math, CH-8092 Zurich, Switzerland

来源：

SIAM JOURNAL ON DISCRETE MATHEMATICS | 2019年 / 33卷 / 01期

关键词：

zero forcing sets; random graphs; graphs with large girth; MINIMUM RANK; VALUES; BOUNDS;

D O I：

10.1137/17M1133051

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A subset S of initially infected vertices of a graph G is called zero forcing if we can infect the entire graph by iteratively applying the following process. At each step, any infected vertex which has a unique uninfected neighbor, infects this neighbor. The zero forcing number of G is the minimum cardinality of a zero forcing set in G. We study the zero forcing number of various classes of graphs, including graphs of large girth, H-free graphs for a fixed bipartite graph H, and random and pseudorandom graphs.

引用

页码：95 / 115

页数：21

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