On the weight of minor faces in triangle-free 3-polytopes

DOI10.7151/dmgt.1877zbMath1339.05112OpenAlexW2314010670MaRDI QIDQ726639

Anna O. Ivanova, Oleg V. Borodin

Publication date: 13 July 2016

Published in: Discussiones Mathematicae. Graph Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.7151/dmgt.1877

zbMATH Keywords

plane graph3-polytopeplane mapstructural propertyweight of face

Mathematics Subject Classification ID

Coloring of graphs and hypergraphs (05C15) Polytopes and polyhedra (52B99) Signed and weighted graphs (05C22)

Related Items (2)

The weight of faces in normal plane maps ⋮ An improvement of Lebesgue's description of edges in 3-polytopes and faces in plane quadrangulations

Cites Work

• Every 3-polytope with minimum degree 5 has a 6-cycle with maximum degree at most 11
• Describing 3-faces in normal plane maps with minimum degree 4
• Describing faces in plane triangulations
• Light \(C_4\) and \(C_5\) in 3-polytopes with minimum degree 5
• Each 3-polytope with minimum degree 5 has a 7-cycle with maximum degree at most 15
• The 7-cycle \(C_{7}\) is light in the family of planar graphs with minimum degree 5
• The vertex-face weight of edges in 3-polytopes
• 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
• 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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