Combinatorics / CONCEPT
Critical Vertices and Private Neighbours
The critical-incidence identity and the private-neighbour estimate are Lemmas 2.1 and 2.3 of Iain Beaton and Ben Cameron, A Tight Upper Bound on the Average Order of Dominating Sets of a Graph, arXiv:2208.10475, attributed there to Beaton and Brown.
Closed
DIRECT PREREQUISITES1
DIRECT CONSEQUENCES3
PROOF DEPTH2
DOCUMENT LINKS0
Deletion and insertion
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
- An obstruction to global coalition universalitystructural-affinity · Closed
- Boundary charging for degree-two verticesstructural-affinity · Closed
- Božović Conjecture 12: limited domination in Sierpiński graphsstructural-affinity · Closed
- Classification by an apex and an opposite labelstructural-affinity · Closed
- Deleting a stem and its leavesstructural-affinity · Closed
- Finite dominating-set averagesstructural-affinity · Closed
- Five paired coalition parts in the height-five binary treestructural-affinity · Closed
- From actual graph subsets to actual path subsetsstructural-affinity · Closed
- Neighbour Replacement for Self-Critical Verticesstructural-affinity · Closed
- One-leaf replication of partial dominating familiesstructural-affinity · Closed
- Real-root configurations of book domination polynomialsstructural-affinity · Closed
- Refutation of Annor Conjecture 14structural-affinity · Closed
- Reversible classification of all labelled subsetsstructural-affinity · Closed
- Rooted decomposition and the connected minus-four familystructural-affinity · Closed
- Stem-block counting for dominating setsstructural-affinity · Closed
- The complete formal generating seriesstructural-affinity · Closed
- The Koch-Narayan bipartite edge bound is falsestructural-affinity · Closed
- The Luiz–Vieira generalized Blanuša closing conjecture is falsestructural-affinity · Closed
- The order-33 integer domination-root minimality claimstructural-affinity · Closed
- The stem-conditioned splitstructural-affinity · Closed
- Trapezohedral minimal 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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