Combinatorics / CONCEPT
Neighbour Replacement for Self-Critical Vertices
The neighbour-replacement argument is the strict critical-incidence comparison in the proof of 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.
Closed
DIRECT PREREQUISITES1
DIRECT CONSEQUENCES2
PROOF DEPTH3
DOCUMENT LINKS0
Domination after deletion
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
- Boundary charging for degree-two verticesstructural-affinity · Closed
- Critical Vertices and Private Neighboursstructural-affinity · Closed
- Deleting a stem and its leavesstructural-affinity · Closed
- Equality Graphs for the Two-Thirds Boundstructural-affinity · Closed
- Real-root configurations of book domination polynomialsstructural-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
- 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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