Add fractional chromatic number (ForMathlib) and the Hall ratio conjecture (disproved) - #5214
Open
henrykmichalewski wants to merge 1 commit into
Open
Conversation
…cture (disproved) - New FormalConjecturesForMathlib/Combinatorics/SimpleGraph/FractionalChromaticNumber.lean: fractional colourings, fractionalColoringWeights, fractionalChromaticNumber; proved that the singleton weighting is a fractional colouring, χ_f ≥ 0 and χ_f ≤ |V|. - New FormalConjectures/Wikipedia/HallRatioConjecture.lean: the Hall ratio; Harris's conjecture χ_f ≤ C·ρ recorded as answer(False) (Dvořák–Ossona de Mendez–Wu; Blumenthal et al.); ρ ≤ χ_f and the unbounded-ratio theorem as variants.
github-actions
Bot
added
wikipedia
for-mathlib
This file contains hidden or bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
Sign up for free
to join this conversation on GitHub.
Already have an account?
Sign in to comment
1 participant
Add this suggestion to a batch that can be applied as a single commit.This suggestion is invalid because no changes were made to the code.Suggestions cannot be applied while the pull request is closed.Suggestions cannot be applied while viewing a subset of changes.Only one suggestion per line can be applied in a batch.Add this suggestion to a batch that can be applied as a single commit.Applying suggestions on deleted lines is not supported.You must change the existing code in this line in order to create a valid suggestion.Outdated suggestions cannot be applied.This suggestion has been applied or marked resolved.Suggestions cannot be applied from pending reviews.Suggestions cannot be applied on multi-line comments.Suggestions cannot be applied while the pull request is queued to merge.Suggestion cannot be applied right now. Please check back later.
Adds the fractional chromatic number (absent from Mathlib and upstream) and Harris's Hall ratio conjecture, recorded as disproved.
ForMathlib — new$|V|$ , hence
FormalConjecturesForMathlib/Combinatorics/SimpleGraph/FractionalChromaticNumber.lean:IsFractionalColoring(nonnegative weights on independent finsets covering every vertex with weight ≥ 1),fractionalColoringWeights,fractionalChromaticNumber(ansInfover ℝ). Proved: the singleton weighting is a fractional colouring of total weightfractionalChromaticNumber_le_card; andfractionalChromaticNumber_nonneg.Problem file —
FormalConjectures/Wikipedia/HallRatioConjecture.lean:hallRatiohall_ratio_conjectureanswer(False)— Dvořák–Ossona de Mendez–Wu 2020; Blumenthal–Lidický–Martin–Norin–Pfender–Volec 2022.variants.hallRatio_le_fractionalChromaticNumbersorry+ reference.variants.unboundedsorry+ referencesfractionalChromaticNumber_le_cardUmbrella regenerated with
scripts/mk_all_formathlib.shand included in the commit.Verification
lake buildof both modules on v4.33.1: clean, all linters pass.🤖 Generated with Claude Code