Volume 30, Issue 2
Intrinsic Knotting of Almost Complete Partite Graphs

Commun. Math. Res., 30 (2014), pp. 183-192.

Published online: 2021-05

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• 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.

• Keywords

intrinsically knotted graph, $∆-Y$ exchange, vertex-expansion.

57M25, 57M27

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• RIS
• TXT
@Article{CMR-30-183, author = {Li , Yang}, title = {Intrinsic Knotting of Almost Complete Partite Graphs}, journal = {Communications in Mathematical Research }, year = {2021}, volume = {30}, number = {2}, pages = {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.

}, issn = {2707-8523}, doi = {https://doi.org/10.13447/j.1674-5647.2014.02.09}, url = {http://global-sci.org/intro/article_detail/cmr/18981.html} }
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 -

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.

Yang Li. (2021). Intrinsic Knotting of Almost Complete Partite Graphs. Communications in Mathematical Research . 30 (2). 183-192. doi:10.13447/j.1674-5647.2014.02.09
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