Combinatorics / CONCEPT
Connected Subgraph Counts at a Bridge
Connected vertex-and-edge subgraphs admit an exact decomposition at a single shared root. Their eccentric counts are invariant under graph isomorphism, and the two endpoint minimum expressions in the bridge transformation satisfy a strict joint inequality.
Closed
DIRECT PREREQUISITES1
DIRECT CONSEQUENCES2
PROOF DEPTH1
DOCUMENT LINKS0
The singleton gives strict root bounds
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
- A Path Hull Without Cut Verticesstructural-affinity · Closed
- Bridge Contraction in Bipartite Graphsstructural-affinity · Closed
- De–Patra Conjecture 2.9structural-affinity · Closed
- Minimal bipartite Erdős–Gyárfás counterexamples have no bridgestructural-affinity · Closed
- Native Bridge and Pendant Countingstructural-affinity · Closed
- The Subgraph Core and Native Blocksstructural-affinity · Closed
Documents & exposition
None recorded in this release.
Other authored & advisory relationships
None recorded in this release.
LIBRARY / RELEASE VERSIONS
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