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Everything about Zarankiewicz problem
Unsolved problem in extremal graph theory
The Zarankiewicz problem, an unsolved problem in mathematics, asks for the largest possible number of edges in a bipartite graph that has a given number of vertices and has no complete bipartite subgraphs of a given size. It belongs to the field of extremal graph theory, a branch of combinatorics, and is named after the Polish mathematician Kazimierz Zarankiewicz, who proposed several special cases of the problem in 1951. Wikipedia →
🧠Start here: a 6-step reading path
- Read the overview: Zarankiewicz problemA 5-minute orientation
- Skim a recent paper: Ramsey numbers and the Zarankiewicz problemInfluential work since 2022
- Pick up a classic book: A problem of ZarankiewiczThe most-reprinted book on the subject
- Read the landmark paper: On a problem of K. ZarankiewiczCited 536 times
- Go sideways: Forbidden subgraph problemA closely related topic
- Go sideways: Erdős–Stone theoremA closely related topic
đź“– Definitions
No dictionary entry for this exact phrase.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
On a problem of K. Zarankiewicz
Ăśber ein Problem von K. Zarankiewicz
An Upper Bound on Zarankiewicz' Problem
A contribution to the Zarankiewicz problem
Spectral Extrema for Graphs: The Zarankiewicz Problem
A bipartite Ramsey problem and the Zarankiewicz numbers
A problem of Zarankiewicz
A new result on the problem of Zarankiewicz
🆕 Influential since 2022
đź“š Books worth reading
- 📕A problem of ZarankiewiczRichard K. Guy · 1967
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
đź”— Related topics
- Forbidden subgraph problem In extremal graph theory, the forbidden subgraph problem is the following problem: given a graph G {\displaystyle G} , find the maximal number of edges…
- Erdős–Stone theorem In extremal graph theory, the Erdős–Stone theorem is an asymptotic result generalising Turán's theorem to bound the number of edges in an H-free graph…
- Turán's brick factory problem Unsolved problem in mathematics Can any complete bipartite graph be drawn with fewer crossings than the number given by Zarankiewicz? More unsolved problems…
- Extremal graph theory Extremal graph theory is a branch of combinatorics, itself an area of mathematics, that lies at the intersection of extremal combinatorics and graph theory…
- Biclique-free graph In graph theory, a branch of mathematics, a t-biclique-free graph is a graph that has no Kt,t (complete bipartite graph with 2t vertices) as a subgraph…
- Kőnig's theorem (graph theory) In the mathematical area of graph theory, Kőnig's theorem, proved by Dénes Kőnig (1931), describes an equivalence between the maximum matching problem…
- Complete bipartite graph In the mathematical field of graph theory, a complete bipartite graph or biclique is a special kind of bipartite graph where every vertex of the first…
- Turán's theorem In graph theory, Turán's theorem bounds the number of edges that can be included in an undirected graph that does not have a complete subgraph of a given…