Bibliographic record
Abstract
Gomory--Hu (GH) trees are a classical sparsification technique for graph connectivity. For an edge-capacitated undirected graph $G=(V,E)$ and subset $Z \subseteq V$ of terminals, a GH tree is an edge-capacitated tree $T=(Z,E(T))$ such that for every $u,v \in Z$, the value of the minimum capacity $uv$ cut in $G$ is the same as in $T$. It is well-known that there does not always exist a GH tree which is a subgraph (or minor if $Z \neq V$) of $G$. We characterize those graph-terminal pairs $(G,Z)$ which always admit such a tree. We show that these are the graphs which have no terminal-$K_{2,3}$ minor, that is, a $K_{2,3}$ minor whose nodes each corresponds to a terminal. We then show that the pairs $(G,Z)$ which forbid such $K_{2,3}$ terminal-minors arise, roughly speaking, from so-called Okamura--Seymour instances, planar graphs whose outside face contains all terminals. One consequence is a result on cut-sufficient pairs $(G,H)$, that is, multiflow instances where the cut condition is sufficient to guarantee a multiflow for any capacity/demand weights on $G/H$. Our results characterize the pairs $(G,Z)$ where $G$ is a graph, $Z \subseteq V(G)$, such that $(G,H)$ is cut-sufficient for any demand graph $H$ on $Z$.
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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 | 0.001 | 0.007 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.002 | 0.001 |
| Scholarly communication | 0.002 | 0.006 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.002 | 0.001 |
| Insufficient payload (model declined to judge) | 0.011 | 0.002 |
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".