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Record W3092789209 · doi:10.1017/9781108649094.004

Topological connectedness and independent sets in graphs

2019· book-chapter· en· W3092789209 on OpenAlex
Penny Haxell

Why this work is in the frame

A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.

fundA Canadian funder is recorded on the work.
no affNo Canadian affiliation: this work is invisible to an affiliation-only frame.
No Canadian affiliation. An affiliation-only frame, the usual design, would never have seen this work. It is one of the works that make the case for inverting the frame.

Bibliographic record

VenueCambridge University Press eBooks · 2019
Typebook-chapter
Languageen
FieldComputer Science
TopicTopological and Geometric Data Analysis
Canadian institutionsnot available
FundersNatural Sciences and Engineering Research Council of Canada
KeywordsSocial connectednessHypergraphCombinatoricsMathematicsLine graphSimplicial complexGraphTopology (electrical circuits)Discrete mathematics

Abstract

fetched live from OpenAlex

An abstract simplicial complex C is said to be k-connected if for each $-1\leq d\leq k$ and each continuous map f from the sphere $S^d$ to ||C|| (the body of the geometric realization of C), the map f can be extended to a continuous map from the ball $B^{d+1}$ to ||C||. In 2000 a link was discovered between the topological connectedness of the independence complex of a graph and various other important graph parameters to do with colouring and partitioning. When the graph represents some other combinatorial structure, for example when it is the line graph of a hypergraph H, this link can be exploited to obtain information such as lower bounds on the matching number of H. Since its discovery there have been many other applications of this phenomenon to combinatorial problems. The aim of this article is to outline this general method and to describe some of its applications.

Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.

Full frame distilled prediction

Teacher imitation

Not calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.

metaresearch head score (Codex)0.000
metaresearch head score (Gemma)0.000
Version: codex-gemma-dda1882f352aValidation status: machine_predicted_unvalidated
Candidate categoriesMeta-epidemiology (narrow)
Consensus categoriesnone
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Theoretical or conceptual · Consensus signal: none
GenreCandidate signal: Other · Consensus signal: Other
Teacher disagreement score0.992
Threshold uncertainty score1.000

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0000.000
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0010.000
Bibliometrics0.0010.000
Science and technology studies0.0000.000
Scholarly communication0.0000.000
Open science0.0010.002
Research integrity0.0000.001
Insufficient payload (model declined to judge)0.0000.000

Machine scores (provisional)

The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.

Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.

Opus teacher head0.023
GPT teacher head0.205
Teacher spread0.182 · how far apart the two teachers sit on this one work
Validation statusscore_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it