Combinatorics / CONCEPT
A flat graph whose clique polynomial has a nonreal root
Four complete four-vertex graphs joined in a ring give a twelve-vertex counterexample to Conjecture 1 of On Clique Roots of Flat Graphs.
Closed
DIRECT PREREQUISITES1
DIRECT CONSEQUENCES0
PROOF DEPTH4
DOCUMENT LINKS0
A twelve-vertex refutation
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 regular biconnected graph with a positive fourth difference of ln(i! N(i))structural-affinity · Closed
- AhanjidehEkimYildizZUpperstructural-affinity · Closed
- Conditional Finite Additive Preservationstructural-affinity · Closed
- FactorCriticalMatchingstructural-affinity · Closed
- Matching Fiber Equivalencestructural-affinity · Closed
- Matching Monomial Fibersstructural-affinity · Closed
- Matching Polynomial Formulastructural-affinity · Closed
- Rectangular Convolution at Alpha Minus One Halfstructural-affinity · Closed
- The extremal matching number for odd degreesstructural-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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