TY - JOUR
T1 - 2-Irreducibility of spatial graphs
AU - Lei, Fengchun
AU - Taniyama, Kouki
AU - Zhang, Gengyu
N1 - Funding Information:
The first author is supported in part by a grant (No.10171024) of NSFC and a grant (HIT.2000.04) of Harbin Institute of Technology.
PY - 2006/1
Y1 - 2006/1
N2 - An embedded graph G in the 3-sphere S3 is called 2-irreducible if there are no separating spheres, cutting spheres, singular separating spheres, singular cutting spheres or 2-cutting spheres of G. Let D be a 2-disk in S3 that is very good for G. Let G' be an embedded graph in S 3 obtained from G by contracting D to a point. We show that if G' is 2-irreducible then G is 2-irreducible. By this criterion certain graphs are easily shown to be 2-irreducible. As an application we show a pair of embedded graphs in the 3-sphere which is distinguished by 2-irreducibility.
AB - An embedded graph G in the 3-sphere S3 is called 2-irreducible if there are no separating spheres, cutting spheres, singular separating spheres, singular cutting spheres or 2-cutting spheres of G. Let D be a 2-disk in S3 that is very good for G. Let G' be an embedded graph in S 3 obtained from G by contracting D to a point. We show that if G' is 2-irreducible then G is 2-irreducible. By this criterion certain graphs are easily shown to be 2-irreducible. As an application we show a pair of embedded graphs in the 3-sphere which is distinguished by 2-irreducibility.
KW - Irreducibility of spatial graph
KW - Spatial graph
UR - http://www.scopus.com/inward/record.url?scp=32644451607&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=32644451607&partnerID=8YFLogxK
U2 - 10.1142/S0218216506004336
DO - 10.1142/S0218216506004336
M3 - Article
AN - SCOPUS:32644451607
SN - 0218-2165
VL - 15
SP - 31
EP - 41
JO - Journal of Knot Theory and its Ramifications
JF - Journal of Knot Theory and its Ramifications
IS - 1
ER -