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Record W4256347034 · doi:10.1002/net.20318

Improper coloring of unit disk graphs

2009· article· en· W4256347034 on OpenAlex

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.

affAt least one author lists a Canadian institution in the pinned OpenAlex snapshot.
fundA Canadian funder is recorded on the work.

Bibliographic record

VenueNetworks · 2009
Typearticle
Languageen
FieldComputer Science
TopicAdvanced Graph Theory Research
Canadian institutionsMcGill University
FundersNatural Sciences and Engineering Research Council of Canada
KeywordsCombinatoricsVertex (graph theory)Complete coloringMathematicsIndifference graphEdge coloringChromatic scaleGraph coloringDiscrete mathematicsChordal graphGraphInterval graphComputer scienceInterval (graph theory)Unit disk1-planar graphLine graphGraph power

Abstract

fetched live from OpenAlex

Abstract Motivated by a satellite communications problem, we consider a generalized coloring problem on unit disk graphs. A coloring is k ‐improper if no more than k neighbors of every vertex have the same colour as that assigned to the vertex. The k ‐improper chromatic number χ k ( G ) is the least number of colors needed in a k ‐improper coloring of a graph G . The main subject of this work is analyzing the complexity of computing χ k for the class of unit disk graphs and some related classes, e.g., hexagonal graphs and interval graphs. We show NP‐completeness in many restricted cases and also provide both positive and negative approximability results. Because of the challenging nature of this topic, many seemingly simple questions remain: for example, it remains open to determine the complexity of computing χ k for unit interval graphs. © 2009 Wiley Periodicals, Inc. NETWORKS, 2009

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 categoriesnone
Consensus categoriesnone
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Theoretical or conceptual · Consensus signal: Theoretical or conceptual
GenreCandidate signal: Empirical · Consensus signal: none
Teacher disagreement score0.896
Threshold uncertainty score0.290

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0000.000
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0000.000
Bibliometrics0.0000.001
Science and technology studies0.0000.000
Scholarly communication0.0000.000
Open science0.0010.000
Research integrity0.0000.000
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 head0.022
GPT teacher head0.284
Teacher spread0.262 · 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