Article ID Journal Published Year Pages File Type
8903898 Journal of Combinatorial Theory, Series B 2018 8 Pages PDF
Abstract
Let G be a 3-partite graph with k vertices in each part and suppose that between any two parts, there is no cycle of length four. Fischer and Matoušek asked for the maximum number of triangles in such a graph. A simple construction involving arbitrary projective planes shows that there is such a graph with (1−o(1))k3/2 triangles, and a double counting argument shows that one cannot have more than (1+o(1))k7/4 triangles. Using affine planes defined by specific planar polynomials over finite fields, we improve the lower bound to (1−o(1))k5/3.
Related Topics
Physical Sciences and Engineering Mathematics Discrete Mathematics and Combinatorics
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