Elsevier

Information Processing Letters

Volume 59, Issue 6, 23 September 1996, Pages 331-333
Information Processing Letters

Intersection number of two connected geometric graphs

https://doi.org/10.1016/0020-0190(96)00124-XGet rights and content

Abstract

Let S be a finite set of points in the plane in general position such that each point of S is colored red or blue. In this paper, we solve the following problem: find two geometric spanning trees of the blue and the red points such that they intersect in as few points as possible. We also prove that there are two paths, one connecting the blue points and the other connecting the red points such that any edge of each of them intersects the other at most once.

References (4)

There are more references available in the full text version of this article.

Cited by (24)

  • Monochromatic plane matchings in bicolored point set

    2020, Information Processing Letters
    Citation Excerpt :

    For bicolored inputs, Merino et al. [10] obtained a tight bound on the number of intersections in monochromatic minimum weight matchings for bicolored point sets. Tokunaga [11] examined non-crossing spanning trees of the red points and the blue points and found a tight bound on the minimum number of intersections between the red and blue spanning trees. Joeris et al. [7] studied the number of intersections for monochromatic planar spanning cycles.

  • Colored spanning graphs for set visualization

    2018, Computational Geometry: Theory and Applications
    Citation Excerpt :

    Borgelt et al. [7] discuss computing planar red-blue minimum spanning trees where edges may connect red and blue points only, and the tree must be planar. Finally, Tokunaga [30] considers a set of red or blue points in the plane and computes two geometric spanning trees of the blue and the red points such that they intersect in as few points as possible. When there are no ties (e.g., if no two edges of the same color have the same length), every red edge in a minimum RBP spanning graph also occurs in a minimum spanning tree of only the red and purple points (since otherwise we could replace it by another red edge of smaller weight).

  • Connecting colored point sets

    2007, Discrete Applied Mathematics
View all citing articles on Scopus
View full text