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TRIANGLE-Y EXCHANGES ON INTRINSIC KNOTTING OF ALMOST COMPLETE AND COMPLETE PARTITE GRAPHS

YANG LI

Department of Applied Mathematics, Beijing Technology and Business University, Beijing, 100048, China

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JIAHU QIN

Research School of Engineering, The Australian National University, Canberra, ACT 2600, Australia

Corresponding author.

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FENGCHUN LEI

School of Mathematical Sciences, Dalian University of Technology, Dalian, 116024, China

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XIANGKE WANG

College of Mechatronics and Automation, National University of Defense Technology, Changsha, 410073, China

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, and

XIHAI ZHANG

School of Engineering, Northeast Agricultural University, Harbin 150030, China

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https://doi.org/10.1142/S021821651100990XCited by:1 (Source: Crossref)

Abstract

Let G be a 0- or 1-deficient graph which is intrinsically knotted, let J represent any graph obtained from G by a finite sequence of Δ-Y exchanges and/or vertex expansions. We prove that removing any vertex of J, and all edges incident to that vertex, yields an intrinsically linked graph. This result provides more intrinsically knotted graphs which satisfy the conjecture mentioned in Adams' The Knot Book that removing any vertex from an intrinsically knotted graph yields an intrinsically linked graph.

Keywords:

AMSC: 57M25, 57M27

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