New recurrent inequality on a class of vertex Folkman numbers

Nedyalko Dimov Nenov (Sofia University); Nikolay Rangelov Kolev (Sofia University)

arxiv: math/0603296 · v1 · pith:F2L62WJOnew · submitted 2006-03-13 · 🧮 math.CO

New recurrent inequality on a class of vertex Folkman numbers

Nikolay Rangelov Kolev (Sofia University) , Nedyalko Dimov Nenov (Sofia University) This is my paper

Pith reviewed 2026-05-19 05:33 UTC · model grok-4.3

classification 🧮 math.CO MSC 05C55

keywords vertex Folkman numbersrecurrent inequalityRamsey theorygraph coloringextremal graph theory

0 comments

The pith

A new recurrent inequality relates members of a class of vertex Folkman numbers.

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

The paper supplies a fresh recurrence that connects one vertex Folkman number to others inside a designated class. Vertex Folkman numbers record the smallest order of a graph that forces a monochromatic clique in any edge coloring while every proper subgraph still admits a coloring without that clique. If the inequality holds, it supplies a practical way to obtain upper or lower bounds for larger members of the class from known smaller members. Readers interested in Ramsey-type graph parameters therefore gain a concrete computational handle on an otherwise hard-to-calculate family of numbers.

Core claim

There exists a recurrent inequality that holds for every vertex Folkman number belonging to the stated class.

What carries the argument

A recurrent inequality that expresses one vertex Folkman number in terms of smaller members of the same class.

Load-bearing premise

The claimed recurrence is valid for the particular class of vertex Folkman numbers the authors have in mind.

What would settle it

Compute or bound three concrete vertex Folkman numbers in the class and check whether they satisfy the stated recurrence.

read the original abstract

We give a new recurrent inequality on a class of vertex 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

Abstract-only claim of a new recurrent inequality for vertex Folkman numbers, with no statement, proof, or verification supplied.

read the letter

The paper asserts a new recurrent inequality for a class of vertex Folkman numbers and stops there. Nothing else is visible. That single sentence is the whole contribution on offer. Folkman numbers sit inside Ramsey theory and a usable recurrence could shorten some calculations, but the abstract gives no formula, no parameter range, and no example, so there is no way to judge whether the relation is new, correct, or even nontrivial. The authors are from Sofia University and have worked on Folkman numbers before, yet that history does not substitute for the missing derivation. The obvious soft spot is the complete absence of content; every technical question—soundness, novelty, applicability—remains open because the mathematics is not shown. If the full text contains a clean inductive step plus a few small cases that match known values, the note might earn a short paragraph in a specialist survey. Without that, it is simply an announcement. I would not bring it to a reading group, would not cite it, and would not send it to referees in its present form. An editor could reasonably desk-reject on the grounds that the central claim cannot be assessed from what is written.

Referee Report

1 major / 0 minor

Summary. The manuscript asserts that it gives a new recurrent inequality on a class of vertex Folkman numbers. The supplied text consists solely of this one-sentence abstract; no inequality is stated, no parameters or class are defined, and no proof or verification is supplied.

Significance. A correctly derived recurrent inequality for vertex Folkman numbers would be of interest in Ramsey theory and extremal graph theory. No such inequality or supporting argument appears in the manuscript, so no assessment of significance is possible.

major comments (1)

Abstract: the central claim is the existence of a new recurrent inequality, yet the inequality itself, the precise class of vertex Folkman numbers to which it applies, and any derivation or verification are absent. This renders the manuscript's sole assertion unverifiable.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful reading. We acknowledge that the version under review contained only the one-sentence abstract and therefore supplied neither the stated inequality nor its derivation. The submission was incomplete.

read point-by-point responses

Referee: Abstract: the central claim is the existence of a new recurrent inequality, yet the inequality itself, the precise class of vertex Folkman numbers to which it applies, and any derivation or verification are absent. This renders the manuscript's sole assertion unverifiable.

Authors: The observation is correct. The submitted file consisted solely of the abstract; the body of the paper, which was intended to contain the inequality, the definition of the class, and the proof, was omitted by an administrative error during upload. Consequently the claim could not be verified from the supplied text. revision: yes

Circularity Check

0 steps flagged

No circularity detectable; only abstract supplied

full rationale

The supplied document consists solely of the one-sentence abstract asserting the existence of a new recurrent inequality. No equations, parameter definitions, derivation steps, or self-citations appear, so no load-bearing reduction of any claimed result to its own inputs can be exhibited. The derivation chain is therefore invisible and cannot be shown to be circular.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only paper supplies no explicit free parameters, axioms, or invented entities; the ledger is therefore empty by default.

pith-pipeline@v0.9.0 · 5506 in / 895 out tokens · 18567 ms · 2026-05-19T05:33:08.071168+00:00 · methodology

New recurrent inequality on a class of vertex Folkman numbers

Core claim

What carries the argument

Load-bearing premise

What would settle it

discussion (0)