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Let F be a set of graphs. The planar Tur\'an number, ex (n, F), is the maximum number of edges in an n-vertex planar graph which does not contain any member of F as a subgraph. In this paper, we give upper bounds of ex (n, \K₄, ₅\) 25/11 (n-2). We also give constructions which show the bounds are tight for infinitely many graphs.
Tao Fang (Mon,) studied this question.
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