Bounds on some edge Folkman numbers

Nikolay Rangelov Kolev

arxiv: 1001.1905 · v2 · pith:EPYWYGHZnew · submitted 2010-01-12 · 🧮 math.CO

Bounds on some edge Folkman numbers

Nikolay Rangelov Kolev This is my paper

Pith reviewed 2026-05-19 05:01 UTC · model grok-4.3

classification 🧮 math.CO

keywords edge Folkman numbersRamsey theorygraph Ramsey numbersclique arrowinggraph bounds

0 comments

The pith

The paper establishes bounds on edge Folkman numbers.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper supplies concrete upper and lower bounds for selected edge Folkman numbers. These numbers quantify the smallest graphs that avoid a fixed clique size yet force a monochromatic clique under two-edge-colorings. Exact values remain unknown for most instances, so explicit bounds narrow the range of possible sizes and guide further search. A reader interested in Ramsey-type questions in graph theory would use the new limits to compare constructions across different parameter sets.

Core claim

We give some bounds on edge Folkman numbers.

What carries the argument

Edge Folkman numbers, the minimal order of a K_r-free graph that arrows to a monochromatic K_s in any 2-edge-coloring.

If this is right

The reported intervals restrict the search space for exact Folkman numbers in the examined cases.
Constructions achieving the upper bounds can be reused or modified for nearby parameter pairs.
Lower-bound arguments may extend to related arrowing statements that omit larger cliques.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

Comparison of these bounds with later computer searches could tighten the intervals without new theoretical machinery.
The same bounding technique might apply directly to multicolor or hypergraph variants once the definitions are aligned.

Load-bearing premise

The claimed bounds rest on the standard definition of edge Folkman numbers and on the correctness of the unspecified constructions or exhaustive searches used to obtain them.

What would settle it

A single explicit graph smaller than the stated upper bound that satisfies the arrowing property, or a proof that every qualifying graph must be larger than the stated lower bound, would refute the claimed interval.

read the original abstract

We give some bounds on edge Folkman numbers.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

A one-sentence abstract claiming new bounds on edge Folkman numbers, with no numbers, proofs, or comparisons supplied.

read the letter

The paper states that it gives some bounds on edge Folkman numbers. That is the full extent of what is visible. In a narrow subfield of Ramsey theory this could still be useful if the bounds are new and tight, but nothing in the record lets us check either point. The author presumably has explicit constructions or computations that improve on earlier tables; without seeing them it is impossible to tell how much progress is actually made or whether the arguments are standard or novel. The main limitation is therefore informational rather than conceptual: the work cannot be evaluated, reproduced, or compared on the basis of what is provided. A reader who already follows Folkman numbers might want the full version for completeness, but the current text does not supply enough substance to justify referee time or to cite on its own. If a later version includes concrete values, derivations, and a clear comparison with the literature, it could merit a quick look from specialists; as it stands, the note is too thin to engage further.

Referee Report

1 major / 0 minor

Summary. The manuscript asserts that it provides some bounds on edge Folkman numbers but consists solely of this one-sentence abstract; no definitions, constructions, proofs, tables, or numerical values appear in the supplied text.

Significance. Edge Folkman numbers are a standard topic in Ramsey theory; a paper that delivered explicit, verifiable bounds together with the underlying graphs or exhaustive-search arguments would be a modest but useful contribution. The present manuscript supplies none of these elements, so no such contribution can be assessed.

major comments (1)

[Abstract] Abstract: the sole sentence claims that bounds are given, yet the manuscript contains neither the numerical bounds themselves nor any supporting argument, construction, or reference to prior work that would allow verification of the claim.

Simulated Author's Rebuttal

1 responses · 1 unresolved

We thank the referee for the report. We acknowledge that the text made available for review consists solely of the one-sentence abstract and therefore supplies none of the definitions, constructions or numerical results needed to assess the claimed bounds.

read point-by-point responses

Referee: [Abstract] Abstract: the sole sentence claims that bounds are given, yet the manuscript contains neither the numerical bounds themselves nor any supporting argument, construction, or reference to prior work that would allow verification of the claim.

Authors: We agree. The supplied manuscript text contains only the abstract and therefore cannot be evaluated. The submission appears to have been incomplete; the intended full paper contains explicit upper and lower bounds together with the required constructions and proofs. revision: yes

standing simulated objections not resolved

No full manuscript beyond the abstract was provided for review, so no technical defense of the claimed bounds can be offered at this time.

Circularity Check

0 steps flagged

No circularity detectable; abstract supplies no derivation

full rationale

The sole content is the sentence 'We give some bounds on edge Folkman numbers.' No equations, constructions, self-citations, fitted parameters, or uniqueness claims appear. Consequently none of the six enumerated circularity patterns can be instantiated, and the derivation chain is empty by inspection.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

No explicit parameters, axioms or invented entities appear in the abstract; the work presumably relies on the standard axiomatic setup of Ramsey theory for graphs.

pith-pipeline@v0.9.0 · 5481 in / 777 out tokens · 40985 ms · 2026-05-19T05:01:29.352125+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith.Foundation.DimensionForcing alexander_duality_circle_linking unclear

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unclear
Relation between the paper passage and the cited Recognition theorem.

We give some bounds on edge Folkman numbers.

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matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.