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Record W2119863390 · doi:10.82308/26339

Odd cycles in planar graphs

2005· dissertation· en· W2119863390 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.

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

VenueeScholarship@McGill (McGill) · 2005
Typedissertation
Languageen
FieldEngineering
TopicOptimization and Packing Problems
Canadian institutionsnot available
FundersNatural Sciences and Engineering Research Council of CanadaMcGill University
KeywordsCombinatoricsComputer scienceMathematics

Abstract

fetched live from OpenAlex

Given a graph G = (V, E), an odd cycle cover is a subset of the vertices whose removal makes the graph bipartite, that is, it meets all odd cycles in G. A packing in G is a collection of vertex disjoint odd cycles. This thesis addresses algorithmic and structural problems concerning odd cycle covers and packings. In particular, we consider the two NP-hard problems of finding a maximum packing and a minimum covering. In 1994 Brass [53] conjectured that tau, the minimum size of an odd cycle cover, is at most twice nu, the maximum size of a packing. The conjecture is known to be false in general [11, 41]. We prove here that tau < 10nu for planar graphs. Our structural results leads to the first constant approximation algorithm for the packing problem. The covering problem was shown to be tractable for graphs of constant sized solutions [42]. We give a linear time algorithm for the covering problem restricted to the case where the graphs have constant sized solutions and are planar.

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: Not applicable · Consensus signal: none
GenreCandidate signal: Empirical · Consensus signal: Empirical
Teacher disagreement score0.771
Threshold uncertainty score0.999

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0000.000
Meta-epidemiology (narrow)0.0010.001
Meta-epidemiology (broad)0.0010.000
Bibliometrics0.0010.001
Science and technology studies0.0000.000
Scholarly communication0.0000.001
Open science0.0010.000
Research integrity0.0010.002
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 head0.012
GPT teacher head0.222
Teacher spread0.210 · 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