combinatorics / Graph domination & zero forcing

TxGraffiti-Davila Conjecture 9

If $G$ is connected, cubic and diamond-free, must the zero-forcing number satisfy $Z(G) \le \gamma(G) + 2$? A connected cubic triangle-free $14$-vertex graph has $Z = 7$ and $\gamma = 4$.

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combinatoricsJun 12, 2026Significance 5/100Registry: unreviewed

TxGraffiti-Davila Conjecture 9

Prior state unknowndisproved

If $G$ is connected, cubic and diamond-free, must the zero-forcing number satisfy $Z(G) \le \gamma(G) + 2$? A connected cubic triangle-free $14$-vertex graph has $Z = 7$ and $\gamma = 4$.

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If $G$ is connected, cubic and diamond-free, must the zero-forcing number satisfy $Z(G) \le \gamma(G) + 2$? A connected cubic triangle-free $14$-vertex graph has $Z = 7$ and $\gamma = 4$.

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