Combinatorics / CONCEPT
Weighted Vertex Products and Closed Walks
On a connected graph over a commutative group with surjective squaring, symmetric edge weights factor into vertex products exactly when every even closed walk balances. For a bipartite graph over any commutative group, every specified spanning tree gives equivalent simple-cycle and fundamental-cycle tests.
Closed
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DIRECT CONSEQUENCES2
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Even Closed Walks Are the Complete Obstruction
RELATIONSHIP ATLAS
Every connection, in context.
Direct recorded relationships
Proof dependencyStructural affinityDocument link
Certified topology / UPSTREAM
Prerequisites
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Certified topology / DOWNSTREAM
Consequences
RELATED KNOWLEDGE
Structural connections
- Actual Even-Cycle Traversalsstructural-affinity · Closed
- Cyclic Transport and Weighted Rankstructural-affinity · Closed
- Rank from Maximum Matchings without Even Simple Cyclesstructural-affinity · Closed
- Ranks of Weighted Paths and Cyclesstructural-affinity · Closed
- Stabilizer Even-Cycle Rank Correctionstructural-affinity · Closed
Documents & exposition
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