Extremal graphs for intersecting triangles
Journal of Combinatorial Theory Series B
New asymptotics for bipartite Tura´n numbers
Journal of Combinatorial Theory Series A
Norm-graphs: variations and applications
Journal of Combinatorial Theory Series B
Turán Numbers of Bipartite Graphs and Related Ramsey-Type Questions
Combinatorics, Probability and Computing
On Arithmetic Progressions of Cycle Lengths in Graphs
Combinatorics, Probability and Computing
Properly colored subgraphs and rainbow subgraphs in edge-colorings with local constraints
Random Structures & Algorithms
Constrained Ramsey numbers of graphs
Journal of Graph Theory
Rainbow Induced Subgraphs in Proper Vertex Colorings
Fundamenta Informaticae
Rainbow Turán problem for even cycles
European Journal of Combinatorics
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For a fixed graph $H$, we define the rainbow Turán number $\ex^*(n,H)$ to be the maximum number of edges in a graph on $n$ vertices that has a proper edge-colouring with no rainbow $H$. Recall that the (ordinary) Turán number $\ex(n,H)$ is the maximum number of edges in a graph on $n$ vertices that does not contain a copy of $H$. For any non-bipartite $H$ we show that $\ex^*(n,H)=(1+o(1))\ex(n,H)$, and if $H$ is colour-critical we show that $\ex^{*}(n,H)=\ex(n,H)$. When $H$ is the complete bipartite graph $K_{s,t}$ with $s \leq t$ we show $\ex^*(n,K_{s,t}) = O(n^{2-1/s})$, which matches the known bounds for $\ex(n,K_{s,t})$ up to a constant. We also study the rainbow Turán problem for even cycles, and in particular prove the bound $\ex^*(n,C_6) = O(n^{4/3})$, which is of the correct order of magnitude.