The path P_n maximizes the number of zero forcing sets of every size k among all distance-hereditary n-vertex graphs, and the conjecture reduces to verifying bounded-order split-prime graphs for graphs with unique prime bags.
The Electronic Journal of Combinatorics25(4), P4.47 (2018)
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The Path-Extremal Conjecture for Zero Forcing: Distance-Hereditary Graphs and a Split-Decomposition Reduction
The path P_n maximizes the number of zero forcing sets of every size k among all distance-hereditary n-vertex graphs, and the conjecture reduces to verifying bounded-order split-prime graphs for graphs with unique prime bags.