trureturingGitHub MATHEMATICAL ATLAS

Combinatorics / CONCEPT

Finite chordality and perfect elimination

The source theorem ranges over V : Type u for any universe u; the existing native predicate ranges over V : Type 0. NativeChordal denotes FaalNonStable.Chordal. Later(G,ord,v) denotes exactly the set of u in V satisfying ord(v) < ord(u) and G.Adj v u. IsPEO has exactly the injective and isClique_later fields. Both finite equivalences include empty and disconnected graphs and require neither a supplied Fintype nor decidable adjacency.

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DIRECT PREREQUISITES2
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THEOREM

An elimination order implies chordality

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Elimination rankings and rooted clique forestsElimination rankings and rootedclique forestsNon-chordal graphs with unstable restricted clique polynomialsNon-chordal graphs withunstable restricted cliquepolynomialsFinite chordality and perfect eliminationFinite chordality and perfectelimination
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Lean sourceResearch workspace
Status
Closed
Depth
2
Layer
D5/S3
Domain
Combinatorics
Node ID
D5/S3/Combinatorics/Graph/Chordal/Characterization
Repository path
D5/S3/Combinatorics/Graph/Chordal/Characterization.lean
Truth release
sha256:76a8db6a0f78609b1b9d4a959c8392f2752f2daaddc1930e046e34ce07d0f608
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b52262a023c4db9bb30a128ebfd80ea4ef4c1a53
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37a24ddf3b9983bdabf0acbfd9b32b06c35c28d3

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Dependency edges, status, and source coordinates come from the verified release and certified topology. Blueprint exposition is labeled separately. A fallback title carries no additional mathematical authority.