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Updated scenarios show 1.5°C overshoot is unavoidable but limitable

Gohar L, Mathison C, Sanderson B, Sandstad M, Smith C, Walsh T, Gillett N, Ribes A, Kikstra J, Nicholls Z, Thiery W, Schleussner C, Rogelj J.   +12 more
europepmc   +1 more source

All Graphs With a Failed Zero Forcing Number of Two [PDF]

Symmetry, 2021
Given a graph G, the zero forcing number of G, Z(G), is the smallest cardinality of any set S of vertices on which repeated applications of the forcing rule results in all vertices being in S. The forcing rule is: if a vertex v is in S, and exactly one neighbor u of v is not in S, then u is added to S in the next iteration.
Darren A Narayan
exaly   +5 more sources

The Zero Forcing Number of Graphs [PDF]

SIAM Journal on Discrete Mathematics, 2019
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 $G$.
Thomas Kalinowski, Benny Sudakov, Nina Kamčev   +2 more
exaly   +5 more sources

Some Bounds on the Zero Forcing Number of a Graph

Discrete Applied Mathematics, 2018
A set $Z$ of vertices of a graph $G$ is a zero forcing set of $G$ if initially labeling all vertices in $Z$ with $1$ and all remaining vertices of $G$ with $0$, and then, iteratively and as long as possible, changing the label of some vertex $u$ from $0$ to $1$ if $u$ is the only neighbor with label $0$ of some vertex with label $1$, results in the ...
Dieter Rautenbach, Michael Gentner
exaly   +3 more sources

Positive Semidefinite Zero Forcing [PDF]

Linear Algebra and Its Applications, 2013
The positive semidefinite zero forcing number Z+(G) of a graph G was introduced in [4]. We establish a variety of properties of Z+(G): Any vertex of G can be in a minimum positive semidefinite zero forcing set (this is not true for standard zero forcing).
Craig Jeremy Erickson, Leslie Hogben, Nathan Wärnberg   +2 more
exaly   +1 more source

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On Extremal Graphs for Zero Forcing Number

Graphs and Combinatorics, 2022
For a graph \(G\) with \(S\subseteq V(G)\), \(S\) is a zero forcing set of \(G\) if iteratively adding vertices to \(S\) from \(V(G)\setminus S\) that are the unique neighbor in \(V(G)\setminus S\) of some vertex in \(S\), results in the entire \(V(G)\) of \(G\).
Yi-Ping Liang, Jianxi Li, Shou-Jun Xu
openaire   +1 more source

On graphs maximizing the zero forcing number

Discrete Applied Mathematics, 2023
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Yi-Ping Liang, Shou-Jun Xu
openaire   +3 more sources

Extremal Values and Bounds for the Zero Forcing Number

Discrete Applied Mathematics, 2016
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Uéverton S Souza, Dieter Rautenbach, Michael Gentner   +2 more
exaly   +4 more sources