Combinatorics / CONCEPT
Equality Graphs for the Two-Thirds Bound
The equality characterization 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. A graph is star-like precisely when every vertex is a leaf or a stem having one or two leaf neighbours.
Closed
DIRECT PREREQUISITES1
DIRECT CONSEQUENCES1
PROOF DEPTH5
DOCUMENT LINKS0
Strictness outside stem blocks
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
- Dominating sets omitting a stemstructural-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
- The stem-conditioned splitstructural-affinity · Closed
- Transporting residual dominationstructural-affinity · Closed
- Two-Thirds Bound for Dominating-Set Averagesstructural-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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