Intersection number of two connected geometric graphs
References (4)
- et al.
Simple alternating path problem
Discrete Math.
(1990) On pairs of disjoint segments in convex position in the plane
Ann. Discrete Math.
(1984)
Cited by (24)
Monochromatic plane matchings in bicolored point set
2020, Information Processing LettersCitation 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.
A note on two geometric paths with few crossings for points labeled by integers in the plane
2018, Discrete MathematicsColored spanning graphs for set visualization
2018, Computational Geometry: Theory and ApplicationsCitation 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).
A note on harmonic subgraphs in labelled geometric graphs
2008, Information Processing LettersConnecting colored point sets
2007, Discrete Applied MathematicsOn plane spanning trees and cycles of multicolored point sets with few intersections
2005, Information Processing Letters