Maximal planar graphs of inscribable type and diagonal flips

A theorem due to Wagner states that given two maximal planar graphs with n vertices, one can be obtained from the other by performing a finite sequence of diagonal flips. In this paper, we show a result of a similar flavour—given two maximal planar graphs of inscribable type having the same vertex s...

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Bibliographic Details
Published inDiscrete mathematics Vol. 309; no. 4; pp. 920 - 925
Main Author Cheung, Kevin K.H.
Format Journal Article
LanguageEnglish
Published Kidlington Elsevier B.V 06.03.2009
Elsevier
Subjects
Applied sciences
Computer science; control theory; systems
Convex and discrete geometry
Diagonal flip
Exact sciences and technology
Geometry
Information retrieval. Graph
Inscribable
Mathematics
Maximal planar graph
Polytope
Sciences and techniques of general use
Theoretical computing
Polytope
Maximal planar graph
Inscribable
Diagonal flip
Vertex
Planar graph
Maximal graph
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Summary:A theorem due to Wagner states that given two maximal planar graphs with n vertices, one can be obtained from the other by performing a finite sequence of diagonal flips. In this paper, we show a result of a similar flavour—given two maximal planar graphs of inscribable type having the same vertex set, one can be obtained from the other by performing a finite sequence of diagonal flips such that all the intermediate graphs are of inscribable type.
ISSN:0012-365X
1872-681X
DOI:10.1016/j.disc.2008.01.038