Full paper in PDF format:
$%M. Ozawa and Y. Tsutsumi, Primitive spatial graphs and graph minors, Rev. Mat. Complut. 20 (2007), no. 2, 391–406.%$

Primitive Spatial Graphs and Graph Minors
Makoto OZAWA and Yukihiro TSUTSUMI
Department of Natural Sciences
Faculty of Arts and Sciences
Komazawa University
1-23-1 Komazawa, Setagaya-ku
Tokyo 154-8525 — Japan
w3c@komazawa-u.ac.jp
Department of Mathematics
Faculty of Science and Technology
Sophia University
Kioicho 7-1, Chiyoda-ku
Tokyo 102-8554 — Japan
tsutsumi@mm.sophia.ac.jp

Received: April 10, 2006
Accepted: February 6, 2007

ABSTRACT

Robertson, Seymour, and Thomas characterized linkless embeddings of graphs by flat embeddings, and determined the obstruction set for linkless embeddings. In this paper, we extend flat embeddings to “primitive embeddings” as linkless embeddings to knotless embeddings. Although the obstruction set for knotless embeddings has not been determined, fundamental theorems and conjectures are obtained.

Key words: spatial graph, graph minor.
2000 Mathematics Subject Classification: primary 57M25, 57M15; secondary 05C83, 05C10.