trureturingGitHub MATHEMATICAL ATLAS

Combinatorics / CONCEPT

The Zero Forcing Number of P(n,3)

Eight vertices are necessary and sufficient to zero-force P(n,3) for every n at least thirteen.

Closed Authored exposition
DIRECT PREREQUISITES9
DIRECT CONSEQUENCES4
PROOF DEPTH8
DOCUMENT LINKS1
THEOREM

Enlarging the initial black set

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External Boundary in P(n,3)External Boundary in P(n,3)Forts and Mask CompletenessForts and Mask CompletenessForts for the outerSpoke AnchorForts for the outerSpoke AnchorForts for the outerNext AnchorForts for the outerNext AnchorForts for the outerPrev AnchorForts for the outerPrev AnchorForts for the innerSpoke AnchorForts for the innerSpoke AnchorForts for the innerNext AnchorForts for the innerNext AnchorForts for the innerPrev AnchorForts for the innerPrev AnchorEvery Ten-Vertex Set Has Boundary at Least EightEvery Ten-Vertex Set HasBoundary at Least EightThe Zero Forcing Number of P(n,3)The Zero Forcing Number ofP(n,3)Radius-Four Column CompressionRadius-Four Column CompressionThe unrestricted grid-power zero-forcing conjecture is falseThe unrestricted grid-powerzero-forcing conjecture isfalseZero forcing powers of equal-legged spidersZero forcing powers of equal-legged spidersOrdinary zero forcing, symmetric maximum nullity, and minimum rank of unequal-leg spider powersOrdinary zero forcing,symmetric maximum nullity, andminimum rank of unequal-leg
Proof dependencyStructural affinityDocument link

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Lean sourceResearch workspace
Status
Closed
Depth
8
Layer
D5/S3
Domain
Combinatorics
Node ID
D5/S3/Combinatorics/GeneralizedPetersen/ZeroForcingThree
Repository path
D5/S3/Combinatorics/GeneralizedPetersen/ZeroForcingThree.lean
Truth release
sha256:76a8db6a0f78609b1b9d4a959c8392f2752f2daaddc1930e046e34ce07d0f608
Source commit
b52262a023c4db9bb30a128ebfd80ea4ef4c1a53
Source tree
37a24ddf3b9983bdabf0acbfd9b32b06c35c28d3

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Dependency edges, status, and source coordinates come from the verified release and certified topology. Blueprint exposition is labeled separately. A fallback title carries no additional mathematical authority.