The Rectilinear Crossing Number of $K_{10}$ is $62$-Reference-Cited by-同舟云学术

The Rectilinear Crossing Number of $K_{10}$ is $62$

Published:2001-04-09 Issue:1 Volume:8 Page:
ISSN:1077-8926
Container-title:The Electronic Journal of Combinatorics
language:
Short-container-title:Electron. J. Combin.

Author:

Brodsky Alex,Durocher Stephane,Gethner Ellen

Abstract

The rectilinear crossing number of a graph $G$ is the minimum number of edge crossings that can occur in any drawing of $G$ in which the edges are straight line segments and no three vertices are collinear. This number has been known for $G=K_n$ if $n \leq 9$. Using a combinatorial argument we show that for $n=10$ the number is 62.

Publisher

The Electronic Journal of Combinatorics

Subject

Computational Theory and Mathematics,Geometry and Topology,Theoretical Computer Science,Applied Mathematics,Discrete Mathematics and Combinatorics

Link

https://www.combinatorics.org/ojs/index.php/eljc/article/download/v8i1r23/pdf

Cited by 9 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. Automated Mathematical Discovery and Verification: Minimizing Pentagons in the Plane;Lecture Notes in Computer Science;2024

2. Chords of 2-Factors in Planar Cubic Bridgeless Graphs;Graphs and Combinatorics;2022-10-17

3. On the crossing number for Kronecker product of a tripartite graph with path;AKCE International Journal of Graphs and Combinatorics;2020-05-01

4. The Rectilinear Crossing Number of K n : Closing in (or Are We?);Thirty Essays on Geometric Graph Theory;2012-10-29

5. The Early History of the Brick Factory Problem;The Mathematical Intelligencer;2010-01-14