Properly Colored Geometric Matchings and 3-Trees Without Crossings on Multicolored Points in the Plane
Let \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$X$$\end{document} be a set of multicolored points in the plane suc...
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Published in | Discrete and Computational Geometry and Graphs Vol. 8845; pp. 96 - 111 |
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Main Authors | , , |
Format | Book Chapter |
Language | English |
Published |
Switzerland
Springer International Publishing AG
01.01.2014
Springer International Publishing |
Series | Lecture Notes in Computer Science |
Subjects | |
Online Access | Get full text |
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Summary: | Let \documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}$$X$$\end{document} be a set of multicolored points in the plane such that no three points are collinear and each color appears on at most \documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}$$\lceil |X|/2 \rceil $$\end{document} points. We show the existence of a non-crossing properly colored geometric perfect matching on \documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}$$X$$\end{document} (if \documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}$$|X|$$\end{document} is even), and the existence of a non-crossing properly colored geometric spanning tree with maximum degree at most \documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}$$3$$\end{document} on \documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}$$X$$\end{document}. Moreover, we show the existence of a non-crossing properly colored geometric perfect matching in the plane lattice. In order to prove these our results, we propose an useful lemma that gives a good partition of a sequence of multicolored points. |
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Bibliography: | M. Kano—Partially supported by Japan Society for the Promotion of Science, Grant-in-Aid for Scientific Research (C).K. Suzuki—Partially supported by MEXT. KAKENHI 24740068.52C35: Arrangements of points, flats, hyperplanes. 05C70: Factorization, matching, partitioning, covering and packing. 05C05: Trees. |
ISBN: | 9783319132860 3319132865 |
ISSN: | 0302-9743 1611-3349 |
DOI: | 10.1007/978-3-319-13287-7_9 |