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Bicubic planar maps

William T. Tutte (1999)

Annales de l'institut Fourier

A numerical function of bicubic planar maps found by the author and colleagues is a special case of a polynomial due to François Jaeger.

Biembeddings of symmetric configurations and 3-homogeneous Latin trades

Mike J. Grannell, Terry S. Griggs, Martin Knor (2008)

Commentationes Mathematicae Universitatis Carolinae

Using results of Altshuler and Negami, we present a classification of biembeddings of symmetric configurations of triples in the torus or Klein bottle. We also give an alternative proof of the structure of 3-homogeneous Latin trades.

Bi-Lipschitz embeddings of hyperspaces of compact sets

Jeremy T. Tyson (2005)

Fundamenta Mathematicae

We study the bi-Lipschitz embedding problem for metric compacta hyperspaces. We observe that the compacta hyperspace K(X) of any separable, uniformly disconnected metric space X admits a bi-Lipschitz embedding in ℓ². If X is a countable compact metric space containing at most n nonisolated points, there is a Lipschitz embedding of K(X) in n + 1 ; in the presence of an additional convergence condition, this embedding may be chosen to be bi-Lipschitz. By way of contrast, the hyperspace K([0,1]) of the...

Characterization of semientire graphs with crossing number 2

D. G. Akka, J. K. Bano (2002)

Mathematica Bohemica

The purpose of this paper is to give characterizations of graphs whose vertex-semientire graphs and edge-semientire graphs have crossing number 2. In addition, we establish necessary and sufficient conditions in terms of forbidden subgraphs for vertex-semientire graphs and edge-semientire graphs to have crossing number 2.

Characterizations of planar plick graphs

V.R. Kulli, B. Basavanagoud (2004)

Discussiones Mathematicae Graph Theory

In this paper we present characterizations of graphs whose plick graphs are planar, outerplanar and minimally nonouterplanar.

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