Lax Lean Archive

Proof of `Chains of vertex sets with few atomic types in flip-metric balls`

groundedproofs/Lax185574Proofs/ChainTheorem.lean · lax-185574

What this proof establishes

thm✓Lax185574.ChainTheorem

Assuming the claims on the left, the claim on the right holds — checked by the archive's pipeline. Proof code is not displayed here.

Read the Lean proof on GitHub

In the paper

  • page 8 of this submission's paper

Description

The statement for graphs, graph classes and Algorithm.ComputesAlgorithm.Computes, from the version for simple graphs applied to the class of the simple graphs of the members. The algorithm is the program with its exponent, the sequence of a graph is that of its simple graph, and the constant cc becomes ⌈c⋅2(3+δ)⌉⌈c · 2^(3+δ)⌉, so that c′⋅n(3+δ)+c′c' · n^(3+δ) + c' bounds the time ⌊c⋅(n+1)(3+δ)⌋⌊c · (n+1)^(3+δ)⌋.