Summary: A classical result on extremal graph theory is the Erdős-Gallai theorem: if a graph on \(n\) vertices has more than \(\frac{(k-1) n}{2}\) edges, then it contains a path of \(k\) edges. Motivated by the result, Erdős and Sós conjectured that under the same condition, the graph should contain every tree of \(k\) edges. A spider is a rooted tree in which each vertex has degree one or two, except for the root. A leg of a spider is a path from the root to a vertex of degree one. Thus, a path is a spider of 1 or 2 legs. From the motivation, it is natural to consider spiders of 3 legs. In this paper, we prove that if a graph on \(n\) vertices has more than \(\frac{(k-1) n}{2}\) edges, then it contains every \(k\)-edge spider of 3 legs, and also, every \(k\)-edge spider with no leg of length more than 4, which strengthens a result of Woźniak on spiders of diameter at most 4; see M. Woźniak [J. Graph Theory 21, No. 2, 229–234 (1996; Zbl 0841.05017)].