Re-embeddings of Maximum 1-Planar Graphs

In this paper, we examine the re-embeddability of maximum 1-planar graphs. In particular, we prove that every optimal 1-planar graph is uniquely 1-embeddable on the sphere except for a sequence of graphs that are minimal with respect to certain reductions. These optimal 1-planar graphs are closely r...

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Bibliographic Details
Published inSIAM journal on discrete mathematics Vol. 24; no. 4; pp. 1527 - 1540
Main Author Suzuki, Yusuke
Format Journal Article
LanguageEnglish
Published Philadelphia Society for Industrial and Applied Mathematics 01.01.2010
Subjects
Graph theory
Graphs
Mathematical analysis
Optimization
Reduction
Spheres
Studies
Theorems
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ISSN0895-4801
1095-7146
DOI10.1137/090746835

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Summary:In this paper, we examine the re-embeddability of maximum 1-planar graphs. In particular, we prove that every optimal 1-planar graph is uniquely 1-embeddable on the sphere except for a sequence of graphs that are minimal with respect to certain reductions. These optimal 1-planar graphs are closely related to their quadrangular subgraphs. We also give a generating theorem for optimal 1-planar graphs. [PUBLICATION ABSTRACT]
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ISSN:0895-4801
1095-7146
DOI:10.1137/090746835