Theo-Conjecture for bridgeless cubic graphs

Let GG be a bridgeless cubic graph, and let n(G)n(G) denote its number of vertices. Assume

n(G)10.n(G)\geq 10.

Theo-Conjecture.

zdmg(G)=n(G).\operatorname{zdmg}(G)=n(G).

This predicts full zombie damage for sufficiently large bridgeless cubic graphs. The paper proves full damage for cubic graphs of girth at least five, while short cycles may create competing geodesic moves; the bridgeless case with n(G)10n(G)\geq10 remains open.

Sources & referencesView supporting material

Primary source

Randy Davila, “The Zombie Damage Number of a Graph”, arXiv:2607.16382 (2026).

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