Combinatorics / CONCEPT
Stem-block counting for dominating sets
Stem blocks group a stem with all its leaf neighbours. The local counting estimate is Lemma 2.6 of Iain Beaton and Ben Cameron, A Tight Upper Bound on the Average Order of Dominating Sets of a Graph, arXiv:2208.10475. Distinct blocks are disjoint, with the two endpoint descriptions of a two-leaf component identified.
Closed
DIRECT PREREQUISITES1
DIRECT CONSEQUENCES1
PROOF DEPTH3
DOCUMENT LINKS0
Substitution preserves domination
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
- Critical Vertices and Private Neighboursstructural-affinity · Closed
- Deleting a stem and its leavesstructural-affinity · Closed
- Equality Graphs for the Two-Thirds Boundstructural-affinity · Closed
- Neighbour Replacement for Self-Critical Verticesstructural-affinity · Closed
- Real-root configurations of book domination polynomialsstructural-affinity · Closed
- The Luiz–Vieira generalized Blanuša closing conjecture is falsestructural-affinity · Closed
- Trapezohedral minimal dominationstructural-affinity · Closed
- Two-Thirds Bound for Dominating-Set Averagesstructural-affinity · Closed
Documents & exposition
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