Abstract
A geometric graph G =(V(G),E(G)) is a graph drawn in the plane such that V(G) is a set of points in the plane, no three of which are tollinear, and E(G) is a set of (possibly crossing) straight-line segments whose endpoints belang to V(G). If a geometric graph G is a complete bipartite graph with partite sets A and B, i.e., V(G) = A ∪ B, then G is denoted by K(A, B). Let A and B be two disjoint sets of points in the plane such that |A| = |B| and no three points of A ∪ B are tollinear. Then we show that the geometric complete bipartite graph K(A, B) contains a spanning tree T without crossings such that the maximum degree of T is at most 3.
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References
Abellanas, M., García, J., Hernández, G., Noy, M., Ramos, P.: Bipartite embeddings of trees in the plane. In: North, S.C. (ed.) GD 1996. LNCS, vol. 1190, pp. 1–10. Springer, Heidelberg (1997)
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© 2000 Springer-Verlag Berlin Heidelberg
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Kaneko, A. (2000). On the Maximum Degree of Bipartite Embeddings of Trees in the Plane. In: Akiyama, J., Kano, M., Urabe, M. (eds) Discrete and Computational Geometry. JCDCG 1998. Lecture Notes in Computer Science, vol 1763. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-46515-7_13
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DOI: https://doi.org/10.1007/978-3-540-46515-7_13
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-67181-7
Online ISBN: 978-3-540-46515-7
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