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Related papers: Leaky Forcing: A New Variation of Zero Forcing

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We study a recent variation of zero forcing called leaky forcing. Zero forcing is a propagation process on a network whereby some nodes are initially blue with all others white. Blue vertices can "force" a white neighbor to become blue if…

Combinatorics · Mathematics 2025-08-05 Beth Bjorkman , Lei Cao , Franklin Kenter , Ryan Moruzzi , Carolyn Reinhart , Violeta Vasilevska

Vertex leaky forcing was recently introduced as a new variation of zero forcing in order to show how vertex leaks can disrupt the zero forcing process in a graph. An edge leak is an edge that is not allowed to be forced across during the…

Combinatorics · Mathematics 2020-09-16 Joseph S. Alameda , Juergen Kritschgau , Michael Young

Zero forcing is a process on a graph $G = (V,E)$ in which a set of initially colored vertices,$B_0(G) \subset V(G)$, can color their neighbors according to the color change rule. The color change rule states that if a vertex $v$ can color a…

Combinatorics · Mathematics 2024-11-06 Rebekah Herrman , Grace Wisdom

A leak is a vertex that is not allowed to perform a force during the zero forcing process. Leaky forcing was recently introduced as a new variation of zero forcing in order to analyze how leaks in a network disrupt the zero forcing process.…

Combinatorics · Mathematics 2020-08-18 Joseph S. Alameda , Jürgen Kritschgau , Nathan Warnberg , Michael Young

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 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

Zero forcing is an iterative graph coloring process whereby a colored vertex with a single uncolored neighbor forces that neighbor to be colored. It is NP-hard to find a minimum zero forcing set - a smallest set of initially colored…

Discrete Mathematics · Computer Science 2016-07-05 Boris Brimkov

Zero forcing is a combinatorial game played on a graph with a goal of turning all of the vertices of the graph black while having to use as few "unforced" moves as possible. This leads to a parameter known as the zero forcing number which…

Combinatorics · Mathematics 2012-11-21 Steve Butler , Jason Grout , H. Tracy Hall

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

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

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

Zero forcing is an iterative process on a graph used to bound the maximum nullity. The process begins with select vertices as colored, and the remaining vertices can become colored under a specific color change rule. The goal is to find a…

Combinatorics · Mathematics 2017-09-27 Franklin H. J. Kenter , Jephian C. -H. Lin

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 combinatorial game played on a graph where the goal is to start with all vertices unfilled and to change them to filled at minimal cost. In the original variation of the game there were two options. Namely, to fill any one…

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 a combinatorial game played on a graph with the ultimate goal of changing the colour of all the vertices at minimal cost. Originally this game was conceived as a one player game, but later a two-player version was devised…

Let $G$ be a simple, finite, and undirected graph with vertices each given an initial coloring of either blue or white. Zero forcing on graph $G$ is an iterative process of forcing its white vertices to become blue after a finite…

Combinatorics · Mathematics 2022-02-11 Ma. Nerissa M. Abara , Prince Allan B. Pelayo

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

Zero forcing is an iterative graph coloring process, where given a set of initially colored vertices, a colored vertex with a single uncolored neighbor causes that neighbor to become colored. A zero forcing set is a set of initially colored…

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
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