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Record W2978207776 · doi:10.1016/j.entcs.2019.08.033

On Coloring a Class of Claw-free Graphs

2019· article· en· W2978207776 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

VenueElectronic Notes in Theoretical Computer Science · 2019
Typearticle
Languageen
FieldComputer Science
TopicAdvanced Graph Theory Research
Canadian institutionsWilfrid Laurier University
FundersNatural Sciences and Engineering Research Council of Canada
KeywordsCombinatoricsMathematicsCographChordal graphSplit graphGraph coloring1-planar graphDiscrete mathematicsLine graphPathwidthVertex (graph theory)Edge coloringIndifference graphGraphGraph power

Abstract

fetched live from OpenAlex

Given a set L of graphs, a graph G is L -free if G does not contain any graph in L as an induced subgraph. Recently, Frédéric Maffray and co-authors showed that the problem of coloring { claw , 4 K 1 , K 5 \ e }-free graphs can be solved in polynomial time. In this paper, we investigate a related class of graphs. A hole is an induced cycle of length at least 4. Two vertices x , y of a graph G are twins if for any vertex z different from x and y , xz is an edge if and only if yz is an edge. A hole-twin is the graph obtained from a hole by adding a vertex that forms a twin with some vertex of the hole. Hole-twins, and K 5 \ e , are interesting in their connection with line-graphs. They are among the forbidden subgraphs in the characterization of line-graphs. In this paper, we show there is a polynomial time algorithm to color ( claw , 4 K 1 , hole-twin)-free graphs.

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)0.003
metaresearch head score (Gemma)0.001
Version: codex-gemma-dda1882f352aValidation status: machine_predicted_unvalidated
Candidate categoriesOpen science
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 score0.586
Threshold uncertainty score0.999

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0030.001
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0000.000
Bibliometrics0.0010.003
Science and technology studies0.0000.002
Scholarly communication0.0000.001
Open science0.0060.002
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 head0.008
GPT teacher head0.271
Teacher spread0.263 · 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