A lower bound on the size of universal sets for planar graphs

Author:

Chrobak M.1,Karloff H.2

Affiliation:

1. Department of Mathematics, University of California, Riverside, CA

2. Department of Computer Science, University of Chicago, Chicago, IL

Abstract

A Fáry embedding of a planar graph G is an embedding of G into the plane, no edges crossing, with each edge embedded as a straight line segment. A set A C IR 2 is said to be n-universal if every n -node planar graph has a Fáry embedding into A. We show that any n -universal set has size at least 1.098 n , for sufficiently large n.

Publisher

Association for Computing Machinery (ACM)

Reference1 articles.

Cited by 22 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. An Exponential Bound for Simultaneous Embeddings of Planar Graphs;Graphs and Combinatorics;2023-08-17

2. A Note on Universal Point Sets for Planar Graphs;Lecture Notes in Computer Science;2019

3. On Point Set Embeddings for k-Planar Graphs with Few Bends per Edge;SOFSEM 2019: Theory and Practice of Computer Science;2019

4. Improved Bounds for Drawing Trees on Fixed Points with L-Shaped Edges;Lecture Notes in Computer Science;2018

5. Universal point sets for planar three-trees;Journal of Discrete Algorithms;2015-01

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