Davila’s zero-forcing versus domination bound
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Does a connected cubic diamond-free graph satisfy Z(G)≤γ(G)+2, where Z is its zero-forcing number and γ its domination number? Triangle-free graphs lie within this proposed Davila bound.
Why it matters and what counts as progress
Why it matters: A counterexample tests a proposed additive relation between two graph-control parameters even in a sparse cubic class.
What counts as progress: Prove the inequality for a new subclass or certify a graph whose zero-forcing number exceeds its domination number by more than two.
How the problem developed
- 27 Jun 2024 · Theorem and conjecture [1]
Randy R. Davila Proved Z(G)≤γ(G)+2 for connected cubic claw-free graphs and posed a related conjecture for connected cubic diamond-free graphs.
Demonstrandum research artifact Published a connected cubic diamond-free graph on 14 vertices with domination number 4 and zero-forcing number 7, refuting the stated bound for that class.
AI contribution
AI-found cubic graph refutes Davila’s zero-forcing bound
A connected cubic triangle-free graph on 14 vertices has domination number γ=4 and zero-forcing number Z=7. Since it is diamond-free, Z exceeds Davila’s proposed γ+2 bound.
Sources
- Davila, Another conjecture of TxGraffiti concerning zero forcing and domination in graphs
- Erlbacher, Demonstrandum exact results and checks
- Demonstrandum Conjecture 9 counterexample public record
- Erlbacher, Demonstrandum release and AI-use account
- Davila, zero forcing and domination conjecture
- Erlbacher, archived Demonstrandum July 2026 release
Website timeline
Publication dates and editorial changes.