Pith. Sign in

RECORD

The Sum and Product of Independence Numbers of Graphs and their Line Graphs

PaperPDF from arXiv

data files

Paper breakdownThe authors' claims, conditions and measurements, as JSON Signed receiptProof this review has not been altered
X Bluesky LinkedIn Reddit Hacker News
Susanth C, Sunny Joseph Kalayathankal

Combinatorics · Submitted 20 Sep 2014

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

The authors' main claim In this paper, we study the bounds on the sum and product of the independence numbers of graphs and their line graphs.

how it is stated · asserted 0.72 read the record →

Comment (0) Read on arXiv ↗
Cite ▾
arXiv ID1409.5871 (version 1)
Pith IDVFT5K7OW, Pith's permanent record of this paper and its review
CitationSunny Joseph Kalayathankal, Susanth C. "The Sum and Product of Independence Numbers of Graphs and their Line Graphs." arXiv:1409.5871 (2014). https://pith.science/paper/VFT5K7OW
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-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,246 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.06 · states limitation 0.05 · human participants 0.02 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.06 · compares with prior results 0.29 · mentions code or data availability 0.01.

The abstract, sentence by sentence

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

The bounds on the sum and product of chromatic numbers of a graph and its complement are known as Nordhaus-Gaddum inequalities. In this paper, we study the bounds on the sum and product of the independence numbers of graphs and their line graphs.

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 The bounds on the sum and product of chromatic numbers of a graph and its complement are known as Nordhaus-Gaddum inequalities. background 1.00 0.03 0.02 asserted 1.00
s1 In this paper, we study the bounds on the sum and product of the independence numbers of graphs and their line graphs. contribution 1.00 0.81 0.12 asserted 0.72

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.98.

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

The bounds on the sum and product of chromatic numbers of a graph and its complement are known as Nordhaus-Gaddum inequalities. In this paper, we study the bounds on the sum and product of the independence numbers of graphs and their line graphs.

Human review

How Pith checks papers → · Full audit of this paper →

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

What it cites

Cites as background 1 paper

Discussion

Know something about this paper? Leave a comment, or highlight any passage above to comment on it.