TxGraffiti's claw-free graph zero forcing conjecture

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Let GG be a graph. The parameters Z(G)Z(G) and Z+(G)Z_+(G) denote the standard and positive semidefinite zero forcing numbers of GG, respectively. A graph is claw-free if it has no induced subgraph isomorphic to K1,3K_{1,3}. TxGraffiti's conjecture. If GG is claw-free, then

Z+(G)=Z(G).Z_+(G)=Z(G).

The conjecture proposes that the greater flexibility of positive semidefinite forcing does not reduce the forcing number for claw-free graphs. It is presented as a conjecture generated by the TxGraffiti conjecturing program; its resolution is not established in the supplied source.

References

Primary source

Randy Davila, Houston Schuerger and Ben Small, “A Characterization of Claw-Free Graphs using Zero Forcing Invariants”, arXiv:2412.03463 (2024).

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