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Related papers: The Zero Forcing Number of Twisted Hypercubes

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Zero forcing is a dynamic graph coloring process whereby a colored vertex with a single uncolored neighbor forces that neighbor to be colored. This forcing process has been used to approximate certain linear algebraic parameters, as well as…

Discrete Mathematics · Computer Science 2016-04-05 Boris Brimkov , Randy Davila

The zero forcing process is an iterative graph colouring process in which at each time step a coloured vertex with a single uncoloured neighbour can force this neighbour to become coloured. A zero forcing set of a graph is an initial set of…

Combinatorics · Mathematics 2018-12-18 Deepak Bal , Patrick Bennett , Sean English , Calum MacRury , Paweł Prałat

For a graph $G$ in which vertices are either black or white, a zero forcing process is an iterative vertex color changing process such that the only white neighbor of a black vertex becomes black in the next time step. A zero forcing set is…

Combinatorics · Mathematics 2025-08-26 Hau-Yi Lin , Wu-Hsiung Lin , Gerard Jennhwa Chang

Zero forcing is a graph propagation process for which vertices fill-in (or propagate information to) neighbor vertices if all neighbors except for one, are filled. The zero-forcing number is the smallest number of vertices that must be…

Combinatorics · Mathematics 2024-10-24 Heather LeClair , Tim Spilde , Sarah Anderson , Brenda Kroschel

Zero forcing is an iterative graph coloring process studied for its wide array of applications. In this process, the vertices of the graph are initially designated as blue or white, and a zero forcing set is a set of initially blue vertices…

Combinatorics · Mathematics 2026-03-23 Asher Brown , Mark Hunnell , Za'Kiyah Toomer-Sanders , Sarah Weber

Zero forcing is an iterative graph coloring process where at each discrete time step, a colored vertex with a single uncolored neighbor forces that neighbor to become colored. The zero forcing number of a graph is the cardinality of the…

Discrete Mathematics · Computer Science 2017-02-06 Boris Brimkov , Caleb C. Fast , Illya V. Hicks

The zero forcing number is the minimum number of black vertices that can turn a white graph black following a single neighbour colour forcing rule. The zero forcing number provides topological information about linear algebra on graphs,…

Combinatorics · Mathematics 2021-02-10 Alexei Vazquez

The concept of zero forcing involves a dynamic coloring process by which blue vertices cause white vertices to become blue, with the goal of forcing the entire graph blue while choosing as few as possible vertices to be initially blue. Past…

Combinatorics · Mathematics 2024-09-10 Sara Anderton , Kanno Mizozoe , Houston Schuerger , Andrew Schwartz

Zero forcing is a deterministic iterative graph colouring process in which vertices are coloured either blue or white, and in every round, any blue vertices that have a single white neighbour force these white vertices to become blue. Here…

Combinatorics · Mathematics 2021-03-17 Natalie C. Behague , Trent Marbach , Pawel Pralat

A subset $S$ of initially infected vertices of a graph $G$ is called 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 neighbour, infects…

Combinatorics · Mathematics 2017-06-06 Thomas Kalinowski , Nina Kamčev , Benny Sudakov

Zero forcing can be described as a combinatorial game on a graph that uses a color change rule in which vertices change white vertices to blue. The throttling number of a graph minimizes the sum of the number of vertices initially colored…

Combinatorics · Mathematics 2021-02-23 Joshua Carlson , Juergen Kritschgau

Zero forcing is a process on a graph that colors vertices blue by starting with some of the vertices blue and applying a color change rule. Throttling minimizes the sum of the size of the initial blue vertex set and the number of the time…

Zero forcing is a process on a graph in which the goal is to force all vertices to become blue by applying a color change rule. Throttling minimizes the sum of the number of vertices that are initially blue and the number of time steps…

Combinatorics · Mathematics 2019-03-15 Joshua Carlson

The concept of zero forcing is extended from graphs to uniform hypergraphs in analogy with the way zero forcing was defined as an upper bound for the maximum nullity of the family of symmetric matrices whose nonzero pattern of entries is…

Combinatorics · Mathematics 2018-08-30 Leslie Hogben

A dynamic coloring of the vertices of a graph $G$ starts with an initial subset $S$ of colored vertices, with all remaining vertices being non-colored. At each discrete time interval, a colored vertex with exactly one non-colored neighbor…

Combinatorics · Mathematics 2017-08-18 Randy Davila , Michael Henning

Zero forcing is a process that models the spread of information throughout a graph as white vertices are forced to turn blue using a color change rule. The idea of throttling, introduced in 2013 by Butler and Young, is to optimize the…

Combinatorics · Mathematics 2022-04-11 Jurgen Kritschgau , Josh Carlson

Zero forcing in graphs is a coloring process where a colored vertex can force its unique uncolored neighbor to be colored. A zero forcing set is a set of initially colored vertices capable of eventually coloring all vertices of the graph.…

Combinatorics · Mathematics 2024-05-03 Krishna Menon , Anurag Singh

Zero forcing is a process that colors the vertices of a graph blue by starting with some vertices blue and applying a color change rule. Throttling minimizes the sum of the number of initial blue vertices and the time to color the graph. In…

Combinatorics · Mathematics 2019-09-17 Emelie Curl , Jesse Geneson , Leslie Hogben

The zero forcing number of a simple graph, written $Z(G)$, is a NP-hard graph invariant which is the result of the zero forcing color change rule. This graph invariant has been heavily studied by linear algebraists, physicists, and graph…

Combinatorics · Mathematics 2018-02-12 Randy Davila , Michael Henning

Zero forcing is a binary coloring game on a graph where a set of filled vertices can force non-filled vertices to become filled following a color change rule. In 2008, the zero forcing number of a graph was shown to be an upper bound on its…

Combinatorics · Mathematics 2025-08-12 Thomas R. Cameron , Jonad Pulaj
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