Regular Projections of Knotted Double-Handcuff Graphs

Hanaki, Ryo

doi:10.1142/s0218216509007567

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Cited by 2 publications

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“…However, Huh and Oh showed in that there exists a planar graph which has no SAT embeddings. For example, in Figure , the graph P 5 and the complete graph with four vertices have no SAT embeddings , the double‐handcuff graph also has no SAT embeddings . However, it is open to determine which graphs have an SAT embedding and which graphs have no SAT embeddings.…”

Section: Introductionmentioning

confidence: 99%

On strongly almost trivial embeddings of graphs

Hanaki¹

2011

Journal of Graph Theory

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Abstract:We present four new classes of graphs, two of which every member has a strongly almost trivial embedding, and the other two of which every member has no strongly almost trivial embeddings. We show that the property that a graph has a strongly almost trivial embedding and the property that a graph has no strongly almost trivial embeddings are not inherited by minors. ᭧ 2011 Wiley Periodicals, Inc. J Graph Theory MSC 2010: Primary 57M15, 57M25.

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Section: Introductionmentioning

confidence: 99%

On strongly almost trivial embeddings of graphs

Hanaki¹

2011

Journal of Graph Theory

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Regular projections of the link L6n1

Alba¹,

Ramirez²,

Salazar³

2023

J. Knot Theory Ramifications

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Given a link projection [Formula: see text] and a link [Formula: see text], it is natural to ask whether it is possible that [Formula: see text] is a projection of [Formula: see text]. Taniyama answered this question for the cases in which [Formula: see text] is a prime knot or link with crossing number at most five. Recently, Takimura settled the issue for the knot [Formula: see text]. We answer this question for the case in which [Formula: see text] is the link [Formula: see text].

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Regular Projections of Knotted Double-Handcuff Graphs

Abstract: A finite set of specific knotted double-handcuff graphs is shown to be minimal among those which produce all projections of knotted double-handcuff graphs. In addition, we show that a double-handcuff graph has no strongly almost trivial spatial embeddings.

Cited by 2 publications

References 5 publications

On strongly almost trivial embeddings of graphs

On strongly almost trivial embeddings of graphs

Regular projections of the link L6n1

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