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An improved upper bound on the maximum degree of terminal-pairable complete graphs

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António Girão, Gábor Mészáros

Combinatorics · Submitted 22 Aug 2017

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

The authors' main claim In this short note, we improve the upper bound on the largest $\Delta(n)$ with the property that the complete graph on $n$ vertices is terminal-pairable with respect to any demand multigraph of maximum degree at most $\Delta(n)$.

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arXiv ID1708.06837 (version 1)
Pith IDC7P5ZSPV, Pith's permanent record of this paper and its review
CitationAnt\'onio Gir\~ao, G\'abor M\'esz\'aros. "An improved upper bound on the maximum degree of terminal-pairable complete graphs." arXiv:1708.06837 (2017). https://pith.science/paper/C7P5ZSPV
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,054 input tokens.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.18 · human participants 0.01 · controlled comparison 0.03 · randomized assignment 0.01 · states quantitative result 0.27 · compares with prior results 0.85 · mentions code or data availability 0.01.

The abstract, sentence by sentence

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

A graph $G$ is terminal-pairable with respect to a demand multigraph $D$ on the same vertex set as $G$, if there exists edge-disjoint paths joining the end vertices of every demand edge of $D$. In this short note, we improve the upper bound on the largest $\Delta(n)$ with the property that the complete graph on $n$ vertices is terminal-pairable with respect to any demand multigraph of maximum degree at most $\Delta(n)$. This disproves a conjecture originally stated by Csaba, Faudree, Gy\'arf\'as, Lehel and Schelp.

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 graph $G$ is terminal-pairable with respect to a demand multigraph $D$ on the same vertex set as $G$, if there exists edge-disjoint paths joining the end vertices of every demand edge of $D$. background 1.00 0.07 0.02 asserted 0.99
s1 In this short note, we improve the upper bound on the largest $\Delta(n)$ with the property that the complete graph on $n$ vertices is terminal-pairable with respect to any demand multigraph of maximum degree at most $\Delta(n)$. contribution 0.97 0.96 0.65 asserted 1.00
s2 This disproves a conjecture originally stated by Csaba, Faudree, Gy\'arf\'as, Lehel and Schelp. interpretation 0.62 0.85 0.52 asserted 1.00

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

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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 graph $G$ is terminal-pairable with respect to a demand multigraph $D$ on the same vertex set as $G$, if there exists edge-disjoint paths joining the end vertices of every demand edge of $D$. In this short note, we improve the upper bound on the largest $\Delta(n)$ with the property that the complete graph on $n$ vertices is terminal-pairable with respect to any demand multigraph of maximum degree at most $\Delta(n)$. This disproves a conjecture originally stated by Csaba, Faudree, Gy\'arf\'as, Lehel and Schelp.

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