Combinatorics / CONCEPT
Real-root configurations of book domination polynomials
The literal arXiv v1/v2 all-positive-order book domination-root conjecture fails at the four-cycle.
Closed
DIRECT PREREQUISITES1
DIRECT CONSEQUENCES0
PROOF DEPTH2
DOCUMENT LINKS0
The order-one book contradicts the universal conjecture
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
- Classification by an apex and an opposite labelstructural-affinity · Closed
- Critical Vertices and Private Neighboursstructural-affinity · Closed
- Deleting a stem and its leavesstructural-affinity · Closed
- Finite dominating-set averagesstructural-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
- 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 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
Documents & exposition
None recorded in this release.
Other authored & advisory relationships
None recorded in this release.
LIBRARY / RELEASE VERSIONS
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