Straight line embeddings of rooted star forests in the plane

For every 1 ≤ i ≤ n, let Ti be a rooted star with root vi, where vi is not necessary to be 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. Mailing address Mikio Kano Department of CIS Ibaraki University Hitachi 316 JAPAN e-mail: [email protected] fax: +81-294-37-1429