Topic
Intersection theorem
About: Intersection theorem is a research topic. Over the lifetime, 481 publications have been published within this topic receiving 7559 citations.
Papers published on a yearly basis
1 / 2
Papers
TL;DR: In this paper, a min-max relation for submodular functions on graphs is described, and a new combinatorial minmax equality that unifies and extends results including the matroid intersection theorem and the theorem of Lucchesi and Younger on the minimum number of edges which meet every directed cut in a graph is presented.
Abstract: Publisher Summary This chapter describes a min-max relation for submodular functions on graphs. It proves a new combinatorial min-max equality that unifies and extends results including the matroid intersection theorem and the theorem of Lucchesi and Younger on the minimum number of edges, which meet every directed cut in a graph. The method of proof used in the chapter generalizes the method used to prove the polymatroid intersection theorem and the method used to prove the Lucchesi-Younger Theorem including an idea that Lovasz attributes to Neil Robertson.
554 citations
451 citations
TL;DR: The authors are concerned here with one of the oldest problems in combinatorial extremal theory, which is readily described after they have made a few conventions.
Abstract: We are concerned here with one of the oldest problems in combinatorial extremal theory. It is readily described after we have made a few conventions. ގ denotes the set of
428 citations
TL;DR: A matroid-generalization of the stable marriage theorem is formulated and results of Vande Vate and Rothblum are extended on the bipartite stable matching polytope and the lattice structure of generalized stable matchings are studied.
Abstract: We describe a fixed-point based approach to the theory of bipartite stable matchings. By this, we provide a common framework that links together seemingly distant results, like the stable marriage theorem of Gale and Shapley, the Mendelsohn-Dulmage theorem, the Kundu-Lawler theorem, Tarski's fixed-point theorem, the Cantor-Bernstein theorem, Pym's linking theorem, or the monochromatic path theorem of Sands et al. In this framework, we formulate a matroid-generalization of the stable marriage theorem and study the lattice structure of generalized stable matchings. Based on the theory of lattice polyhedra and blocking polyhedra, we extend results of Vande Vate and Rothblum on the bipartite stable matching polytope.
361 citations
Book•
31 Dec 1976
TL;DR: In this paper, the shape of Z-sets in Q-manifolds of the form $M \times [0, 1]$ is shown to be a near homeomorphism.
Abstract: Preliminaries Z-sets in Q Stability of Q-manifoldsitle> Z-sets in Q-manifolds Q-manifolds of the form $M \times [0, 1)$ Shapes of Z-sets in Q Near homeomorphisms and the Sum Theorem Applications of the Sum Theorem The Splitting Theorem The Handle Straightening Theorem The Triangulation Theorem The Classification Theorem Cell-like mappings The ANR Theorem References Appendix Open problems in infinite-dimensional topology.
318 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 3 |
| 2023 | 3 |
| 2022 | 8 |
| 2021 | 4 |
| 2020 | 8 |
| 2019 | 9 |