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The Explicit Graphs Are Subcubic

Lax920634.SubcubicConstruction · concepts/Lax920634/SubcubicConstruction.lean · lax-920634

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    Natural Language Statement

    Lemma

    Every member HkH_k of the specified zig-zag and path-replacement family is subcubic. A port has at most two neighbors inside its path and one neighbor across the regular graph's edge involution.

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    Proven claimDefinitionThis conceptRelated conceptA → B: B builds on A
    Evidence

    Each proof establishes this claim relative to its assumptions.

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    1import Lax920634.ZigZagConstruction
    2
    3/-!
    4---
    5title: The Explicit Graphs Are Subcubic
    6type: lemma
    7---
    8Every member HkH_k of the specified zig-zag and path-replacement family is
    9subcubic. A port has at most two neighbors inside its path and one neighbor
    10across the regular graph's edge involution.
    11
    12# Formalization notes
    13
    14The statement concerns the precise executable construction on `Fin (order k)`.
    15Self-loops and coincident edges are removed by the simple graph definition.
    16-/
    17
    18namespace Lax920634.SubcubicConstruction
    19
    20open ZigZagConstruction EdgeExpansion
    21
    22/-- The specified deterministic family has maximum degree at most three. -/
    23axiom subcubic (k : ℕ) : IsSubcubic (graph k)
    24
    25end Lax920634.SubcubicConstruction
    26
    Show Proof
    Formalization notes

    The statement concerns the precise executable construction on Fin(orderk)Fin (order k). Self-loops and coincident edges are removed by the simple graph definition.

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