On graphs which have locally complete 2-edge-colourings and their relationship to proper circular-arc graphs
Bibliographic record
Abstract
ABSTRACT A 2‐edge‐coloured graph is called locally complete if for each vertex , the vertices adjacent to through edges of the same colour induce a complete subgraph in . Locally complete 2‐edge‐coloured graphs have nice properties, and there exists a polynomial algorithm to decide whether such a graph has an alternating hamiltonian cycle, where alternating means that the colour of two consecutive edges on the cycle are different. Graphs which have locally complete 2‐edge colourings are one of two types of claw‐free perfect graphs indecomposable via clique‐cutsets. In this paper, we characterize the graphs which have locally complete 2‐edge‐colourings by a forbidden substructure, analogous to the one given by Gallai for cocomparability graphs. Our characterization implies a polynomial time recognition algorithm for this class of graphs. We compare the graphs which have locally complete 2‐edge‐colourings with proper interval graphs and proper circular‐arc graphs (which are the graphs having local tournament orientations). We characterize proper interval graphs and proper circular‐arc graphs which have locally complete 2‐edge‐colourings by forbidden subgraphs.
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.
How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.004 |
| Meta-epidemiology (narrow) | 0.000 | 0.001 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.001 | 0.004 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.004 | 0.000 |
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.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".