Combinatorics / CONCEPT
Two-Thirds Bound for Dominating-Set Averages
The inequality is Theorem 2.9 of Iain Beaton and Ben Cameron, A Tight Upper Bound on the Average Order of Dominating Sets of a Graph, arXiv:2208.10475. Stem blocks are grouped by their vertex sets, so a two-vertex component gives one block.
Closed
DIRECT PREREQUISITES2
DIRECT CONSEQUENCES2
PROOF DEPTH4
DOCUMENT LINKS0
Private neighbours remain residual
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 perp hyperplane and classical hexagon intersectionsstructural-affinity · Closed
- Critical Vertices and Private Neighboursstructural-affinity · Closed
- Dominating sets omitting a stemstructural-affinity · Closed
- Equality Graphs for the Two-Thirds Boundstructural-affinity · Closed
- Neighbour Replacement for Self-Critical Verticesstructural-affinity · Closed
- Stem-block counting for dominating setsstructural-affinity · Closed
- The local average at a stemstructural-affinity · Closed
- The Luiz–Vieira generalized Blanuša closing conjecture is falsestructural-affinity · Closed
- The one-copy hub isomorphismstructural-affinity · Closed
Documents & exposition
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Other authored & advisory relationships
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