Combinatorics / CONCEPT
A cone with a linear remainder
Let H be a finite family of three-element subsets of a finite vertex type. Disjoint-union uniqueness means that two disjoint members determine their unordered pair uniquely from their union. Fix a vertex c and suppose the triples avoiding c form a linear family. The link G at c may have arbitrarily large degrees. Its edges and the linear remainder give exact counts for both pair supports of H.
Closed
DIRECT PREREQUISITES1
DIRECT CONSEQUENCES0
PROOF DEPTH4
DOCUMENT LINKS1
The graph support estimate
RELATIONSHIP ATLAS
Every connection, in context.
Direct recorded relationships
Proof dependencyStructural affinityDocument link
Certified topology / UPSTREAM
Prerequisites
Certified topology / DOWNSTREAM
Consequences
None recorded in this release.
RELATED KNOWLEDGE
Structural connections
- Charging saturated link componentsstructural-affinity · Closed
- Exact stars at a marked packetstructural-affinity · Closed
- Fifteen-vertex separation and the fourteen-vertex boundstructural-affinity · Closed
- Ownership at a marked exchangestructural-affinity · Closed
- Reciprocal fibers and actual link componentsstructural-affinity · Closed
- The component correction identitystructural-affinity · Closed
- Two incidence counts and the codegree-four boundstructural-affinity · Closed
- Unordered wedges and four-edge common linksstructural-affinity · Closed
Documents & exposition
Other authored & advisory relationships
None recorded in this release.
LIBRARY / RELEASE VERSIONS
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