Combinatorics / CONCEPT
Residual graphs after positive private deletion
Let G be any finite simple graph with a proper coloring c:V->Fin(3). A vertex is mixed when it has two neighbors of different colors. Its reciprocal debt is 1/6-(1/2)sum_{x in N_G(w)}1/(degree_G(x)+1), in rational arithmetic. Deleting a nonempty set of positive-debt private mixed vertices preserves the mixed-degree condition and excludes singleton color leaves.
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Mixed degrees and singleton color leaves
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Proof dependencyStructural affinityDocument link
Certified topology / UPSTREAM
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Certified topology / DOWNSTREAM
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RELATED KNOWLEDGE
Structural connections
- Actual deletion and global balancestructural-affinity · Closed
- Local graphs and owned triangle rowsstructural-affinity · Closed
- Mixed vertices and actual triangle packetsstructural-affinity · Closed
- Payment for marked triangle rowsstructural-affinity · Closed
- Reciprocal estimates for singleton color leavesstructural-affinity · Closed
- Small mixed graph inequalitystructural-affinity · Closed
- Small mixed-population certificatestructural-affinity · Closed
- Weighted induced deletionstructural-affinity · Closed
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