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On Minrank and the Lov\'asz Theta Function

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Ishay Haviv

Data Structures and Algorithms · Submitted 12 Feb 2018

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

The authors' main claim This implies a limitation on the $\vartheta$-function-based algorithmic approach to approximating the minrank parameter of graphs.

how it is stated · asserted 0.97 read the record →

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arXiv ID1802.03920 (version 2)
Pith IDKNCUDJB6, Pith's permanent record of this paper and its review
CitationIshay Haviv. "On Minrank and the Lov\'asz Theta Function." arXiv:1802.03920 (2018). https://pith.science/paper/KNCUDJB6
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,610 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.39 · human participants 0.01 · controlled comparison 0.03 · randomized assignment 0.01 · states quantitative result 0.95 · compares with prior results 0.77 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

Two classical upper bounds on the Shannon capacity of graphs are the $\vartheta$-function due to Lov\'asz and the minrank parameter due to Haemers. We provide several explicit constructions of $n$-vertex graphs with a constant $\vartheta$-function and minrank at least $n^\delta$ for a constant $\delta>0$ (over various prime order fields). This implies a limitation on the $\vartheta$-function-based algorithmic approach to approximating the minrank parameter of graphs. The proofs involve linear spaces of multivariate polynomials and the method of higher incidence matrices.

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 Two classical upper bounds on the Shannon capacity of graphs are the $\vartheta$-function due to Lov\'asz and the minrank parameter due to Haemers. background 1.00 0.03 0.03 asserted 1.00
s1 We provide several explicit constructions of $n$-vertex graphs with a constant $\vartheta$-function and minrank at least $n^\delta$ for a constant $\delta>0$ (over various prime order fields). result 0.59 0.97 0.60 asserted 1.00
s2 This implies a limitation on the $\vartheta$-function-based algorithmic approach to approximating the minrank parameter of graphs. interpretation 1.00 0.78 0.60 asserted 0.97
s3 The proofs involve linear spaces of multivariate polynomials and the method of higher incidence matrices. method 1.00 0.84 0.03 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

What was examined, and what was not

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not examined
  • full text
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  • references and citing sentences
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  • P abstract
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  • 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

Two classical upper bounds on the Shannon capacity of graphs are the $\vartheta$-function due to Lov\'asz and the minrank parameter due to Haemers. We provide several explicit constructions of $n$-vertex graphs with a constant $\vartheta$-function and minrank at least $n^\delta$ for a constant $\delta>0$ (over various prime order fields). This implies a limitation on the $\vartheta$-function-based algorithmic approach to approximating the minrank parameter of graphs. The proofs involve linear spaces of multivariate polynomials and the method of higher incidence matrices.

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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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