Realizing Planar Graphs as Convex Polytopes

DOI10.1007/978-3-642-25878-7_23zbMath1311.68125OpenAlexW114669477WikidataQ56555111 ScholiaQ56555111MaRDI QIDQ3223957

Günter Rote

Publication date: 9 March 2012

Published in: Graph Drawing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-642-25878-7_23

zbMATH Keywords

convex polytopespiderweb embedding

Mathematics Subject Classification ID

Graph theory (including graph drawing) in computer science (68R10) Computer graphics; computational geometry (digital and algorithmic aspects) (68U05) Planar graphs; geometric and topological aspects of graph theory (05C10) Graph representations (geometric and intersection representations, etc.) (05C62)

Cites Work

• Small grid embeddings of 3-polytopes
• Strictly convex drawings of planar graphs
• Existence and uniqueness of packings with specified combinatorics
• A quantitative Steinitz' theorem
• On the maximal number of edges of convex digital polygons included into an \(m \times m\)-grid
• On the complexity of optimization problems for 3-dimensional convex polyhedra and decision trees
• Steinitz representations of polyhedra and the Colin de Verdière number
• Embedding stacked polytopes on a polynomial-size grid
• Realization spaces of polytopes
• Convex Representations of Graphs
• On the Number of Spanning Trees a Planar Graph Can Have
• How to Draw a Graph
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