Let denote the maximum number of edges in a graph on vertices which does not contain as a subgraph. Let denote a path consisting of vertices and let denote disjoint copies of . In this paper we count .
@article{bwmeta1.element.ojs-doi-10_17951_a_2014_68_1_21, author = {Halina Bielak and Sebastian Kieliszek}, title = {The Tur\'an number of the graph $3P\_4$ }, journal = {Annales Universitatis Mariae Curie-Sk\l odowska, sectio A -- Mathematica}, volume = {68}, year = {2014}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.ojs-doi-10_17951_a_2014_68_1_21} }
Halina Bielak; Sebastian Kieliszek. The Turán number of the graph $3P_4$ . Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica, Tome 68 (2014) . http://gdmltest.u-ga.fr/item/bwmeta1.element.ojs-doi-10_17951_a_2014_68_1_21/
Bushaw, N., Kettle, N., Turán numbers of multiple paths and equibipartite forests, Combin. Probab. Comput. 20 (2011), 837-853.
Erdős, P., Gallai, T., On maximal paths and circuits of graphs, Acta Math. Acad. Sci. Hungar. 10 (1959), 337-356.
Faudree, R. J., Schelp, R. H., Path Ramsey numbers in multicolorings, J. Combin. Theory Ser. B 19 (1975), 150-160.
Gorgol, I., Turán numbers for disjoint copies of graphs, Graphs Combin. 27 (2011), 661-667.
Harary, F., Graph Theory, Addison-Wesley, Mass.-Menlo Park, Calif.-London, 1969.