2024/02/14 by Ben Cameron, Jeannette Janssen, Cameron, Ben +5
Computer Science · Mathematics · #Advanced Topology and Set Theory #Combinatorics (math.CO) #FOS: Mathematics #Mathematical Biology Tumor Growth #Reinforcement Learning in Robotics
paper · pdf · doi:10.48550/arxiv.2402.08866
openalex publication_date 2024/02/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
We give an algorithm that finds a zero forcing set which approximates the optimal size by a factor of pw(G)+1, where pw(G) is the pathwidth of G. Starting from a path decomposition, the algorithm runs in O(nm) time, where n and m are the order and size of the graph, respectively. As a corollary, we obtain a new upper bound on the zero forcing number in terms of the fort number and the pathwidth. The algorithm is based on a correspondence between zero forcing sets and forcing arc sets. This correspondence leads to a new bound on the zero forcing number in terms of vertex cuts, and to new, short proofs for known bounds on the zero forcing number.