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Monotone Drawings of 3-Connected Plane Graphs

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Algorithms - ESA 2015

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9294))

Abstract

A monotone drawing of a graph G is a straight-line drawing of G such that, for every pair of vertices u,w in G, there exists a path P uw in G that is monotone on some line l uw . (Namely, the order of the orthogonal projections of the vertices in P uw on l uw is the same as the order they appear in P uw .) In this paper, we show that the classical Schnyder drawing of 3-connected plane graphs is a monotone drawing on a grid of size f ×f (f ≤ 2n − 5 is the number of internal faces of G), which can be constructed in O(n) time. It also has the advantage that, for any given vertices u,w, the monotone line l uw can be identified in O(1) time.

Research supported in part by NSF Grant CCR-1319732.

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Authors and Affiliations

  1. Department of Computer Science and Engineering, State University of New York at Buffalo, Buffalo, NY, 14260, USA

    Xin He & Dayu He

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  1. Xin He
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  2. Dayu He
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Correspondence to Xin He .

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Editors and Affiliations

  1. University of Technology, Eindhoven, The Netherlands

    Nikhil Bansal

  2. Sapienza University of Rome, Rome, Italy

    Irene Finocchi

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He, X., He, D. (2015). Monotone Drawings of 3-Connected Plane Graphs. In: Bansal, N., Finocchi, I. (eds) Algorithms - ESA 2015. Lecture Notes in Computer Science(), vol 9294. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-48350-3_61

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  • DOI: https://doi.org/10.1007/978-3-662-48350-3_61

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-48349-7

  • Online ISBN: 978-3-662-48350-3

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