Geodesic
The Turán Number of the Graph 2P5
Discussiones Mathematicae. Graph Theory, Tome 36 (2016) no. 3, pp. 683-694.

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We give the Turán number ex (n, 2P5) for all positive integers n, improving one of the results of Bushaw and Kettle [Turán numbers of multiple paths and equibipartite forests, Combininatorics, Probability and Computing, 20 (2011) 837-853]. In particular we prove that ex (n, 2P5) = 3n−5 for n ≥ 18.
Keywords: forest, tree, Turán number 
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Bielak, Halina; Kieliszek, Sebastian. The Turán Number of the Graph 2P5. Discussiones Mathematicae. Graph Theory, Tome 36 (2016) no. 3, pp. 683-694. http://geodesic.mathdoc.fr/item/DMGT_2016_36_3_a12/

[1] N. Bushaw and N. Kettle, Turán numbers of multiple paths and equibipartite forests, Combin. Probab. Comput. 20 (2011) 837-853. doi:10.1017/S0963548311000460

[2] P. Erdős and T. Gallai, On maximal paths and circuits of graphs, Acta Math. Acad. Sci. Hungar. 10 (1959) 337-356. doi:10.1007/BF02024498

[3] R.J. Faudree and R.H. Schelp, Path Ramsey numbers in multicolorings, J. Combin. Theory Ser. B 19 (1975) 150-160. doi:10.1016/0095-8956(75)90080-5

[4] I. Gorgol, Turán numbers for disjoint copies of graphs, Graphs Combin. 27 (2011) 661-667. doi:10.1007/s00373-010-0999-5

[5] F. Harary, Graph Theory (Addison-Wesley, 1969).