Geodesic
New structures and their applications to variants of zero forcing and propagation time
Leslie Hogben1 ; Mark Hunnell2 ; Kevin Liu3 ; Houston Schuerger4 ; Ben Small ; Yaqi Zhang5
1Iowa State University and American Institute of Mathematics
2Winston-Salem State University
3University of Washington
4Trinity College
5Drexel University
The electronic journal of combinatorics, Tome 32 (2025) no. 2
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We introduce a generalization of the concept of a chronological list of forces, called a relaxed chronology. This concept is used to introduce a new way of formulating the standard zero forcing process, which we refer to as parallel increasing path covers, or PIPs. The combinatorial properties of PIPs are utilized to identify bounds comparing standard zero forcing propagation time to positive semidefinite propagation time. A collection of paths within a set of PSD forcing trees, called a path bundle, is used to identify the PSD forcing analog of the reversal of a standard zero forcing process, as well as to draw a connection between PSD forcing and rigid-linkage forcing.
DOI : 10.37236/12237
Classification : 05C15, 05C69, 05C70
Mots-clés : PSD forcing number, power domination number, RL-forcing number

Leslie Hogben  1   ; Mark Hunnell  2   ; Kevin Liu  3   ; Houston Schuerger  4   ; Ben Small    ; Yaqi Zhang  5

1 Iowa State University and American Institute of Mathematics
2 Winston-Salem State University
3 University of Washington
4 Trinity College
5 Drexel University 
@article{10_37236_12237,
     author = {Leslie Hogben and Mark Hunnell and Kevin Liu and Houston Schuerger and Ben Small and Yaqi Zhang},
     title = {New structures and their applications to variants of zero forcing and propagation time},
     journal = {The electronic journal of combinatorics},
     year = {2025},
     volume = {32},
     number = {2},
     doi = {10.37236/12237},
     zbl = {1565.05039},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/12237/}
}
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Leslie Hogben; Mark Hunnell; Kevin Liu; Houston Schuerger; Ben Small; Yaqi Zhang. New structures and their applications to variants of zero forcing and propagation time. The electronic journal of combinatorics, Tome 32 (2025) no. 2. doi: 10.37236/12237

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