Author

Ben Howerton

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Preprint Aug 2026

A Two-Player Zero Forcing Game

We introduce a competitive two-player zero forcing game on a connected graph. Alice and Bob alternately seed white vertices or perform legal zero forces in their own colours, and each player seeks to minimise their own number of seeds. A force preservation rule prevents avoidable blocking of an opponent's established f...

Dickson Y. B. Annor, Ben Howerton · 0 citations

Preprint Jul 2026

Induced Subgraph Bounds on the Zero Forcing Number and Chromatic Consequences

Let $G$ be a graph with chromatic number $\chi(G)$, clique number $\omega(G)$ and zero forcing number $Z(G)$. We establish new lower bounds on $Z(G)$ in terms of induced triangle-free subgraphs. In particular, we show that if a graph $G$ contains an induced triangle-free subgraph $H$ with minimum degree $\delta(H) \ge...

Dickson Y. B. Annor, Ben Howerton · 0 citations