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arXiv · 1509.02883

Fractional Zero Forcing via Three-color Forcing Games

Leslie Hogben·Kevin F. Palmowski·David E. Roberson·Michael Young
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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.

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Leslie Hogben, Kevin F. Palmowski, David E. Roberson, Michael Young. 2015-09-09. Fractional Zero Forcing via Three-color Forcing Games. https://doi.org/10.1016/j.dam.2016.05.004

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