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Arboricity and Acyclic Chromatic Number

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Paper breakdownThe authors' claims, conditions and measurements, as JSON Signed receiptProof this review has not been altered
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Oliver Knill

Combinatorics · Submitted 6 Nov 2023

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We can improve this HMS inequality by 1, if acy(G) is even.

how it is stated · asserted 0.96 read the record →

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arXiv ID2311.03049 (version 1)
Pith ID7KXKFYJJ, Pith's permanent record of this paper and its review
CitationOliver Knill. "Arboricity and Acyclic Chromatic Number." arXiv:2311.03049 (2023). https://pith.science/paper/7KXKFYJJ
Claim paper

The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Open the compiled record

Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,942 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.16 · human participants 0.02 · controlled comparison 0.06 · randomized assignment 0.01 · states quantitative result 0.93 · compares with prior results 0.92 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

A theorem of Hakimi, Mitchem and Schmeichel from 1996 states that the edge arboricity arb(G) of a graph is bounded above by the acyclic chromatic number acy(G). We can improve this HMS inequality by 1, if acy(G) is even. We review also results about acyclic chromatic numbers in the context of a Gr\"unbaum conjecture from 1973.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 A theorem of Hakimi, Mitchem and Schmeichel from 1996 states that the edge arboricity arb(G) of a graph is bounded above by the acyclic chromatic number acy(G). background 1.00 0.02 0.08 asserted 1.00
s1 We can improve this HMS inequality by 1, if acy(G) is even. result 0.76 0.88 0.71 asserted 0.96
s2 We review also results about acyclic chromatic numbers in the context of a Gr\"unbaum conjecture from 1973. background 0.75 0.34 0.04 asserted 0.66

What kind of paper the classifier reports this is: theoretical result 0.99 · evidence from proof or derivation 0.50.

What was examined, and what was not

sources read
  • arXiv listing abstract v1
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
levels run
  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

A theorem of Hakimi, Mitchem and Schmeichel from 1996 states that the edge arboricity arb(G) of a graph is bounded above by the acyclic chromatic number acy(G). We can improve this HMS inequality by 1, if acy(G) is even. We review also results about acyclic chromatic numbers in the context of a Gr\"unbaum conjecture from 1973.

Human review

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How the literature uses it

What this paper does with the arXiv papers it cites

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

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