Combinatorics / CONCEPT
Five paired coalition parts in the height-five binary tree
The perfect binary tree of height five has a paired coalition partition with five parts. Odd part sizes exclude paired domination of individual parts, while four explicit perfect matchings certify their unions. Thus its paired coalition number is at least five, contradicting the value three in Conjecture 1.
Closed
DIRECT PREREQUISITES1
DIRECT CONSEQUENCES0
PROOF DEPTH1
DOCUMENT LINKS0
The conjecture is false
RELATIONSHIP ATLAS
Every connection, in context.
Direct recorded relationships
Proof dependencyStructural affinityDocument link
Certified topology / UPSTREAM
Prerequisites
Certified topology / DOWNSTREAM
Consequences
None recorded in this release.
RELATED KNOWLEDGE
Structural connections
- A Dom-Path Longer Than the Jaco Graph Diameter Boundstructural-affinity · Closed
- An obstruction to global coalition universalitystructural-affinity · Closed
- Božović Conjecture 12: limited domination in Sierpiński graphsstructural-affinity · Closed
- Critical Vertices and Private Neighboursstructural-affinity · Closed
- Finite dominating-set averagesstructural-affinity · Closed
- Refutation of Annor Conjecture 14structural-affinity · Closed
- Regular Graph Covers and Dominationstructural-affinity · Closed
- The Koch-Narayan bipartite edge bound is falsestructural-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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