Review of: Modern Graph Theory by Béla Bollobás
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.
Bibliographic record
Abstract
Graph Theory is still a relatively young subject, and debate still rages on what material constitutes the core results that any introductory text should include. Bollobás has chosen to introduce graph theory - including recent results - in a way that emphasizes the connections between (for example) the Tutte polynomial of a graph, the partition functions of theoretical physics, and the new knot polynomials, all of which are interconnected.On the other hand, graph theory is also rooted strongly in computing science, where it is applied to many different problems; Bollobás's treatment is completely theoretical and does not address these applications. Or, in more practical terms, he is concerned whether a solution exists, rather than asking whether the solution can be computed in a reasonably efficient manner.One of the pleasures of working in graph theory is the abundance of problems available to solve. Unlike many more traditional areas of Mathematics, knowing the core results and proofs is frequently insufficient. Often solving a new problem requires a new approach, or a subtle twist on an existing one, combined with some bare knuckle work. Bollobás emphasizes this in the problems available at the end of each chapter; he includes in total 639 problems, ranging from the reasonably straightforward to the very difficult. I spent time with friends working on these problems, and was intrigued by the variety of the proofs that we came up with.
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 imitationNot 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.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.003 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 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 it