Intrinsic Knotting of Almost Complete Partite Graphs

Intrinsic Knotting of Almost Complete Partite Graphs

Year:    2014

Author:    Yang Li

Communications in Mathematical Research , Vol. 30 (2014), Iss. 2 : pp. 183–192

Abstract

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' 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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.13447/j.1674-5647.2014.02.09

Communications in Mathematical Research , Vol. 30 (2014), Iss. 2 : pp. 183–192

Published online:    2014-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    10

Keywords:    intrinsically knotted graph $∆-Y$ exchange vertex-expansion.

Author Details

Yang Li