The Link Component Number of Suspended Trees

Endo, Takahiro

doi:10.1007/s00373-010-0936-7

Cited by 4 publications

(1 citation statement)

References 11 publications

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“…if G is embedded in the plane, the real projective plane or the torus. For many families of planar graphs, their link component numbers have been determined, see, for example, [5,8,14,15].…”

Section: Introductionmentioning

confidence: 99%

Extremal embedded graphs

Yan¹,

X²

2019

Ars Math. Contemp.

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Let G be a ribbon graph and µ(G) be the number of components of the virtual link formed from G as a cellularly embedded graph via the medial construction. In this paper we first prove that µ(G) ≤ f (G)+γ(G), where f (G) and γ(G) are the number of boundary components and Euler genus of G, respectively. A ribbon graph is said to be extremal if µ(G) = f (G) + γ(G). We then obtain that a ribbon graph is extremal if and only if its Petrial is plane. We introduce a notion of extremal minor and provide an excluded extremal minor characterization for extremal ribbon graphs. We also point out that a related result in the monograph by Ellis-Monaghan and Moffatt is not correct and prove that two related conjectures raised by Huggett and Tawfik hold for more general ribbon graphs.

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Section: Introductionmentioning

confidence: 99%

Extremal embedded graphs

Yan¹,

X²

2019

Ars Math. Contemp.

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The Number of Circles of a Maximum State of a Plane Graph with Applications

Cheng

et al. 2021

Acta Math. Appl. Sin. Engl. Ser.

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Determining the Component Number of Links Corresponding to Triangular and Honeycomb Lattices

Jiang

Deng

2012

J. Knot Theory Ramifications

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There is a classical correspondence between edge-signed plane graphs and link diagrams. Determining component number of links corresponding to plane graphs may be one of the first problems in studying links by using graphs. There has been several early studies in this aspect, for example, the component number of links formed from 2-dimensional square lattices (44) has been determined. In this paper, we determine the component number of links corresponding to 2-dimensional triangular (36) and honeycomb (63) lattices with free or cyclic boundary condition.

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The Link Component Number of Suspended Trees

Abstract: This paper provides a relationship between a geometric structure of a suspended tree and the number of link components of the associated link diagram.

Cited by 4 publications

References 11 publications

Extremal embedded graphs

Extremal embedded graphs

The Number of Circles of a Maximum State of a Plane Graph with Applications

Determining the Component Number of Links Corresponding to Triangular and Honeycomb Lattices

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