Abstract
AbstractWe introduce a new approach and prove that the maximum number of triangles in a ‐free graph on vertices is at most We show a connection to ‐uniform hypergraphs without (Berge) cycles of length less than six, and estimate their maximum possible size. Using our approach, we also (slightly) improve the previous estimate on the maximum size of an induced‐‐free and ‐free graph.
Highlights
We show a connection to r‐uniform hypergraphs without (Berge) cycles of length less than six, and estimate their maximum possible size
Motivated by a conjecture of Erdős [3] on the maximum possible number of pentagons in a triangle‐free graph, Bollobás and Győri [2] initiated the study of the natural converse of this problem
Applying our approach to the 2‐shadow of a hypergraph of girth at least six, we prove the following result
Summary
Triangles in C5free graphs and hypergraphs of girth six Ergemlidze, Beka; Methuku, Abhishek.
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