## Tokyo Journal of Mathematics

### Knots in Certain Spatial Graphs

Miki SHIMABARA

#### Abstract

In 1983, J. H. Conway and C. McA. Gordon showed in [1] that every embedding of the complete graph $K_7$ in the three-dimensional Euclidean space $\mathbf{R}^3$ contains a knotted cycle. In this paper we generalize their method and show that every embedding of the complete bipartite graph $K_{5,5}$ in $\mathbf{R}^3$ contains a knotted cycle.

#### Article information

Source
Tokyo J. of Math., Volume 11, Number 2 (1988), 405-413.

Dates
First available in Project Euclid: 1 April 2010

https://projecteuclid.org/euclid.tjm/1270133985

Digital Object Identifier
doi:10.3836/tjm/1270133985

Mathematical Reviews number (MathSciNet)
MR976575

Zentralblatt MATH identifier
0669.57001

#### Citation

SHIMABARA, Miki. Knots in Certain Spatial Graphs. Tokyo J. of Math. 11 (1988), no. 2, 405--413. doi:10.3836/tjm/1270133985. https://projecteuclid.org/euclid.tjm/1270133985