The DOI matches its Crossref record; 10 of the 10 references it cites were found in a registry or an index.
The Sandwich Theorem
Abstract
This report contains expository notes about a function $\theta(G)$ that is popularly known as the Lovász number of a graph $G$. There are many ways to define $\theta(G)$, and the surprising variety of different characterizations indicates in itself that $\theta(G)$ should be interesting. But the most interesting property of $\theta(G)$ is probably the fact that it can be computed efficiently, although it lies "sandwiched" between other classic graph numbers whose computation is NP-hard. I have tried to make these notes self-contained so that they might serve as an elementary introduction to the growing literature on Lovász's fascinating function.
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
Cites
Bollobás, B. (1985) · Cited by 6,196
Geometric Algorithms and Combinatorial Optimization
Grötschel, M., Lovász, L., & Schrijver, A. (1988) · Algorithms and Combinatorics · doi:10.1007/978-3-642-97881-4 · Cited by 3,431
The ellipsoid method and its consequences in combinatorial optimization
Grötschel, M., Lovász, L., & Schrijver, A. (1981) · Combinatorica · doi:10.1007/bf02579273 · Cited by 2,011
On the Shannon capacity of a graph
Lovasz, L. (1979) · IEEE Transactions on Information Theory · doi:10.1109/tit.1979.1055985 · Cited by 1,624
Cones of Matrices and Set-Functions and 0–1 Optimization
Lovász, L., & Schrijver, A. (1991) · SIAM Journal on Optimization · doi:10.1137/0801013 · Cited by 1,008
Interior Point Methods in Semidefinite Programming with Applications to Combinatorial Optimization
Alizadeh, F. (1995) · SIAM Journal on Optimization · doi:10.1137/0805002 · Cited by 892
Unitary Triangularization of a Nonsymmetric Matrix
Householder, A. S. (1958) · Journal of the ACM · doi:10.1145/320941.320947 · Cited by 629
On the facial structure of set packing polyhedra
Padberg, M. W. (1973) · Mathematical Programming · doi:10.1007/bf01580121 · Cited by 596
An Algorithmic Theory of Numbers, Graphs and Convexity
Lovász, L. (1986) · Society for Industrial and Applied Mathematics eBooks · doi:10.1137/1.9781611970203 · Cited by 358
Large-Scale Optimization of Eigenvalues
Overton, M. L. (1992) · SIAM Journal on Optimization · doi:10.1137/0802007 · Cited by 209
Cited by
Optimal Reconstruction Codes for Deletion Channels
Chrisnata, J., Kiah, H. M., & Yaakobi, E. (2020) · arXiv · doi:10.48550/arxiv.2004.06032 · Cited by 14
Metadata
- Authors
- Knuth, D. E.
- Venue
- The Electronic Journal of Combinatorics
- Published
- 1994-04-13
- Volume
- 1
- Issue
- 1
- ISSN
- 1077-8926 (ISSN-L)
- OpenAlex
- W1548134571
- Cited by
- 296
- References
- 10
- FWCI
- 6.30
- Type
- journal article
- Language
- en
- Open access
- closed
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
How to cite
Cite CoChat for the checks on this page, and the paper for its own findings.
- This page
- CoChat. (2026). Citation check: The Sandwich Theorem. https://app.cochat.ai/papers/10.37236/1193
- The paper
- Knuth, D. E. (1994). The Sandwich Theorem. The Electronic Journal of Combinatorics. https://doi.org/10.37236/1193
Data sources
Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
