Article
Fractional Zero Forcing via Three-color Forcing Games
Discrete Applied Mathematics
Document Type
Article
Disciplines
Publication Version
Accepted Manuscript
Publication Date
11-20-2016
DOI
10.1016/j.dam.2016.05.004
Abstract
An r-fold analogue of the positive semidefinite zero forcing process that is carried out on the r-blowup of a graph is introduced and used to define the fractional positive semidefinite forcing number. Properties of the graph blowup when colored with a fractional positive semidefinite forcing set are examined and used to define a three-color forcing game that directly computes the fractional positive semidefinite forcing number of a graph. We develop a fractional parameter based on the standard zero forcing process and it is shown that this parameter is exactly the skew zero forcing number with a three-color approach. This approach and an algorithm are used to characterize graphs whose skew zero forcing number equals zero.
Creative Commons License
Creative Commons Attribution-NonCommercial-No Derivative Works 4.0 International
Copyright Owner
Elsevier B.V.
Copyright Date
2016
Language
en
File Format
application/pdf
Citation Information
Leslie Hogben, Kevin F. Palmowski, David E. Roberson and Michael Young. "Fractional Zero Forcing via Three-color Forcing Games" Discrete Applied Mathematics Vol. 213 (2016) p. 114 - 129 Available at: http://works.bepress.com/leslie-hogben/30/
This is a manuscript of an article published as Hogben, Leslie, Kevin F. Palmowski, David E. Roberson, and Michael Young. "Fractional zero forcing via three-color forcing games." Discrete Applied Mathematics 213 (2016): 114-129. DOI: 10.1016/j.dam.2016.05.004. Posted with permission.