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Results tagged with graph-theory
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user 97131
Questions about the branch of combinatorics called graph theory (not to be used for questions concerning the graph of a function). This tag can be further specialized via using it in combination with more specialized tags such as extremal-graph-theory, spectral-graph-theory, algebraic-graph-theory, topological-graph-theory, random-graphs, graph-colorings and several others.
4
votes
1
answer
382
views
Turan numbers of r-partite hypergraphs
Let $H$ be a balanced $r$-partite $r$-uniform hypergraph with $nr$ vertices. (Each part of this hypergraph consists of $n$ vertices; every hyperedge has exactly one vertex in each part.) Denote a comp …
- 155
2
votes
2
answers
2k
views
Maximum number of edges in bipartite graph without cycles of length 4
Let $ex(n,H)$ denote the maximum number of edges of a graph on $n$ vertices not containing a copy of $H$. Let $ex(n,m,H)$ denote the maximum number of edges of a bipartite graph with parts' sizes $m$ …
- 1,687
2
votes
Accepted
Maximum number of edges in bipartite graph without cycles of length 4
I find out that this problem is a special case of Zarankiewicz problem and it was solved by István Reiman in 1958 (thanks to Oliver Krüger for correction). The answer is $ex(n,n,C_4)\sim n^{3/2}$.
- 251