trureturingGitHub MATHEMATICAL ATLAS

Quantum / CONCEPT

Condensation need not preserve LC-equivalence

Two connected six-vertex graphs are related by local complementations and satisfy the bound of at most one outside neighbour for every vertex of the condensation set in both graphs, but their condensed graphs are not LC-equivalent. This refutes Conjecture 16 of Vandré, de Jong, Hahn, Burchardt, Gühne and Pappa.

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Six vertices refute the conjecture

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The forbidden-subgraph conjecture for MMI in graph statesThe forbidden-subgraphconjecture for MMI in graphstatesCondensation need not preserve LC-equivalenceCondensation need not preserveLC-equivalence
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Lean sourceResearch workspace
Status
Closed
Depth
1
Layer
D5/S3
Domain
Quantum
Node ID
D5/S3/Quantum/Entanglement/GraphCondensationLCRefutation
Repository path
D5/S3/Quantum/Entanglement/GraphCondensationLCRefutation.lean
Truth release
sha256:76a8db6a0f78609b1b9d4a959c8392f2752f2daaddc1930e046e34ce07d0f608
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b52262a023c4db9bb30a128ebfd80ea4ef4c1a53
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37a24ddf3b9983bdabf0acbfd9b32b06c35c28d3

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