TY - JOUR
T1 - Intrinsic Knotting of Almost Complete Partite Graphs
AU - Li , Yang
JO - Communications in Mathematical Research 
VL - 2
SP - 183
EP - 192
PY - 2021
DA - 2021/05
SN - 30
DO - http://doi.org/10.13447/j.1674-5647.2014.02.09
UR - https://global-sci.org/intro/article_detail/cmr/18981.html
KW - intrinsically knotted graph, $∆-Y$ exchange, vertex-expansion.
AB - <p style="text-align: justify;">Let $G$ be a complete $p$-partite graph with 2 edges removed, $p ≥ 7$, which is
intrinsically knotted. Let $J$ represent any graph obtained from $G$ by a finite sequence
of $∆-Y$ exchanges and/or vertex expansions. In the present paper, we show that
the removal of any vertex of $J$ and all edges incident to that vertex produces an
intrinsically linked graph. This result offers more intrinsically knotted graphs which
hold for the conjecture presented in Adams&#39; book (Adams C. The Knot Book. New
York: W. H. Freeman and Company, 1994), that is, the removal of any vertex from
an intrinsically knotted graph yields an intrinsically linked graph.</p>