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Chromatic roots and limits of dense graphs

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Peter Csikvari, Peter E. Frenkel, Jan Hladky, Tamas Hubai

Combinatorics · Submitted 30 Nov 2015

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

The authors' main claim In this short note we observe that recent results of Abert and Hubai and of Csikvari and Frenkel about Benjamini--Schramm continuity of the holomorphic moments of the roots of the chromatic polynomial extend to the theory of dense graph sequences.

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arXiv ID1511.09429 (version 2)
Pith IDQZWAWDUW, Pith's permanent record of this paper and its review
CitationJan Hladky, Peter Csikvari, Peter E. Frenkel, Tamas Hubai. "Chromatic roots and limits of dense graphs." arXiv:1511.09429 (2015). https://pith.science/paper/QZWAWDUW
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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.

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,295 input tokens.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.18 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.03 · compares with prior results 0.80 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; .

In this short note we observe that recent results of Abert and Hubai and of Csikvari and Frenkel about Benjamini--Schramm continuity of the holomorphic moments of the roots of the chromatic polynomial extend to the theory of dense graph sequences. We offer a number of problems and conjectures motivated by this observation.

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 In this short note we observe that recent results of Abert and Hubai and of Csikvari and Frenkel about Benjamini--Schramm continuity of the holomorphic moments of the roots of the chromatic polynomial extend to the theory of dense graph sequences. result 0.91 0.75 0.87 asserted 1.00
s1 We offer a number of problems and conjectures motivated by this observation. future work 0.84 0.82 0.06 asserted 0.72

What kind of paper the classifier reports this is: position or commentary 0.57 · evidence from argument 0.43.

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  • 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

In this short note we observe that recent results of Abert and Hubai and of Csikvari and Frenkel about Benjamini--Schramm continuity of the holomorphic moments of the roots of the chromatic polynomial extend to the theory of dense graph sequences. We offer a number of problems and conjectures motivated by this observation.

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