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On Degree Sum Conditions and Vertex-Disjoint Chorded Cycles

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Bradley Elliott, Ronald Gould, Kazuhide Hirohata

Combinatorics · Submitted 20 Nov 2019

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

The authors' main claim We prove that if $G$ is a graph of sufficiently large order and $\sigma_t(G)\geq 3kt-t+1$ with $k\geq 1$, then $G$ contains $k$ vertex-disjoint chorded cycles.

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arXiv ID1911.08686 (version 1)
Pith IDCHQH5F7F, Pith's permanent record of this paper and its review
CitationBradley Elliott, Kazuhide Hirohata, Ronald Gould. "On Degree Sum Conditions and Vertex-Disjoint Chorded Cycles." arXiv:1911.08686 (2019). https://pith.science/paper/CHQH5F7F
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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, 4,218 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.45 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.98 · compares with prior results 0.12 · mentions code or data availability 0.01.

The abstract, sentence by sentence

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

In this paper, we consider a general degree sum condition sufficient to imply the existence of $k$ vertex-disjoint chorded cycles in a graph $G$. Let $\sigma_t(G)$ be the minimum degree sum of $t$ independent vertices of $G$. We prove that if $G$ is a graph of sufficiently large order and $\sigma_t(G)\geq 3kt-t+1$ with $k\geq 1$, then $G$ contains $k$ vertex-disjoint chorded cycles. We also show that the degree sum condition on $\sigma_t(G)$ is sharp. To do this, we also investigate graphs without chorded cycles.

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 paper, we consider a general degree sum condition sufficient to imply the existence of $k$ vertex-disjoint chorded cycles in a graph $G$. contribution 0.85 0.77 0.10 asserted 0.49
s1 Let $\sigma_t(G)$ be the minimum degree sum of $t$ independent vertices of $G$. background 0.87 0.29 0.02 asserted 0.79
s2 We prove that if $G$ is a graph of sufficiently large order and $\sigma_t(G)\geq 3kt-t+1$ with $k\geq 1$, then $G$ contains $k$ vertex-disjoint chorded cycles. result 0.99 0.96 0.94 asserted 1.00
s3 We also show that the degree sum condition on $\sigma_t(G)$ is sharp. result 0.96 0.95 0.09 asserted 1.00
s4 To do this, we also investigate graphs without chorded cycles. method 0.84 0.89 0.02 asserted 0.77

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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  • 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 paper, we consider a general degree sum condition sufficient to imply the existence of $k$ vertex-disjoint chorded cycles in a graph $G$. Let $\sigma_t(G)$ be the minimum degree sum of $t$ independent vertices of $G$. We prove that if $G$ is a graph of sufficiently large order and $\sigma_t(G)\geq 3kt-t+1$ with $k\geq 1$, then $G$ contains $k$ vertex-disjoint chorded cycles. We also show that the degree sum condition on $\sigma_t(G)$ is sharp. To do this, we also investigate graphs without chorded cycles.

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