Straight line embeddings of rooted star forests in the plane Original Research Article

For every 1⩽i⩽n, let Ti be a rooted star with root vi, where vi is not necessarily its center. Then the union F=T1∪T2∪⋯∪Tn is called a rooted star forest with roots v1,v2,…,vn. Let P be a set of |F| points in the plane in general position containing n specified points p1,p2,…,pn, where |F| denotes the order of F. Then we show that there exists a bijection φ:V(F)→P such that φ(vi)=pi for all 1⩽i⩽n, φ(x) and φ(y) are joined by a straight-line segment if and only if x and y are joined by an edge of F, and such that no two straight-line segments intersect except at their common end-point.