Combinatorics / CONCEPT
Mixed vertices and actual triangle packets
Let V be any finite vertex type and H a finite disjoint-union-free family of subsets of V. Fix a member e of cardinality three. The actual local graph records replacements of one coordinate of e by a vertex outside e. Its mixed vertices correspond precisely to triangle packets containing e in the designated row. The other members of H need not have cardinality three.
Closed
DIRECT PREREQUISITES2
DIRECT CONSEQUENCES1
PROOF DEPTH3
DOCUMENT LINKS1
Exact local-to-packet correspondence
RELATIONSHIP ATLAS
Every connection, in context.
Direct recorded relationships
Proof dependencyStructural affinityDocument link
Certified topology / UPSTREAM
Prerequisites
Certified topology / DOWNSTREAM
Consequences
RELATED KNOWLEDGE
Structural connections
- Actual deletion and global balancestructural-affinity · Closed
- Disjoint-union uniqueness and intersecting linksstructural-affinity · Closed
- Exact stars at a marked packetstructural-affinity · Closed
- Local graphs and owned triangle rowsstructural-affinity · Closed
- Local graphs and reciprocal double countingstructural-affinity · Closed
- Ownership at a marked exchangestructural-affinity · Closed
- Payment for marked triangle rowsstructural-affinity · Closed
- Reciprocal estimates for singleton color leavesstructural-affinity · Closed
- Residual graphs after positive private deletionstructural-affinity · Closed
- The exact triple forcing thresholdstructural-affinity · Closed
- Three-color incidence and population reductionstructural-affinity · Closed
- Three-color reciprocal inequalitystructural-affinity · Closed
- Weighted induced deletionstructural-affinity · Closed
Documents & exposition
Other authored & advisory relationships
None recorded in this release.
LIBRARY / RELEASE VERSIONS
Content history
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