Describing faces in plane triangulations

DOI10.1016/j.disc.2013.11.021zbMath1280.05027OpenAlexW1972670378MaRDI QIDQ394346

Oleg V. Borodin, Anna O. Ivanova, Alexandr V. Kostochka

Publication date: 27 January 2014

Published in: Discrete Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.disc.2013.11.021

zbMATH Keywords

planar graphweightplane triangulation3-polytopestructure propertiesLebesgue's theorem

Mathematics Subject Classification ID

Planar graphs; geometric and topological aspects of graph theory (05C10) Signed and weighted graphs (05C22)

Related Items (23)

The height of faces of 3-polytopes ⋮ A Steinberg-like approach to describing faces in 3-polytopes ⋮ An analogue of Franklin's theorem ⋮ The weight of faces in normal plane maps ⋮ Another tight description of faces in plane triangulations with minimum degree 4 ⋮ Combinatorial structure of faces in triangulations on surfaces ⋮ Heights of minor faces in 3-polytopes ⋮ Light \(C_4\) and \(C_5\) in 3-polytopes with minimum degree 5 ⋮ Tight description of faces of triangulations on the torus ⋮ The vertex-face weight of edges in 3-polytopes ⋮ More about the height of faces in 3-polytopes ⋮ Describing 4-paths in 3-polytopes with minimum degree 5 ⋮ An improvement of Lebesgue's description of edges in 3-polytopes and faces in plane quadrangulations ⋮ On the weight of minor faces in triangle-free 3-polytopes ⋮ Every triangulated 3-polytope of minimum degree 4 has a 4-path of weight at most 27 ⋮ Heights of minor faces in triangle-free 3-polytopes ⋮ Low edges in 3-polytopes ⋮ Low minor faces in 3-polytopes ⋮ Tight description of faces in torus triangulations with minimum degree 5 ⋮ Describing faces in 3-polytopes with no vertices of degree from 5 to 7 ⋮ Low faces of restricted degree in 3-polytopes ⋮ Note on 3-paths in plane graphs of girth 4 ⋮ Tight Descriptions of 3‐Paths in Normal Plane Maps

Cites Work

• Describing 3-faces in normal plane maps with minimum degree 4
• The 7-cycle \(C_{7}\) is light in the family of planar graphs with minimum degree 5
• Light graphs in families of polyhedral graphs with prescribed minimum degree, face size, edge and dual edge weight
• Triangles with restricted degrees of their boundary vertices in plane triangulations
• Triangles with restricted degree sum of their boundary vertices in plane graphs
• Triangulated \(3\)-polytopes without faces of low weight
• Cyclic degrees of 3-polytopes
• Heavy paths, light stars, and big melons
• Light subgraphs of graphs embedded in the plane. A survey
• Colorings of plane graphs: a survey
• Weight of faces in plane maps
• Cyclic coloration of 3-polytopes
• Height of minor faces in plane normal maps
• Unavoidable set of face types for planar maps
• Light subgraphs in planar graphs of minimum degree 4 and edge‐degree 9
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