Diagonal flips in triangulations on closed surfaces with minimum degree at least 4

DOI10.1006/jctb.1998.1889zbMath0934.05046OpenAlexW1988787815MaRDI QIDQ1305524

Atsuhiro Nakamoto, Hideo Komuro, Seiya Negami

Publication date: 10 April 2000

Published in: Journal of Combinatorial Theory. Series B (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jctb.1998.1889

zbMATH Keywords

surfacespheretriangulationsgenusdiagonal flipimbedded graph

Mathematics Subject Classification ID

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

Related Items (12)

Planar triangulations which quadrangulate other surfaces ⋮ Flippable edges in triangulations on surfaces ⋮ Diagonal flips in plane graphs with triangular and quadrangular faces ⋮ \(N\)-flips in 4-connected even triangulations on the sphere ⋮ Generating 4-connected even triangulations on the sphere ⋮ On local transformations in plane geometric graphs embedded on small grids ⋮ Unnamed Item ⋮ Facial achromatic number of triangulations on the sphere ⋮ Generating All Triangulations of Plane Graphs (Extended Abstract) ⋮ \(N\)-flips in even triangulations on surfaces ⋮ Maximal planar graphs of inscribable type and diagonal flips ⋮ Acute triangles in triangulations on the plane with minimum degree at least 4

Cites Work

• All 2-manifolds have finitely many minimal triangulations
• Graph minors. XX: Wagner's conjecture
• Irreducible triangulations of surfaces
• Diagonal flips of triangulations on closed surfaces preserving specified properties
• Diagonal flips in triangulations of surfaces
• Three nonisomorphic triangulations of an orientable surface with the same complete graph
• Diagonal transformations in quadrangulations and Dehn twists preserving cycle parities
• Irreducible triangulations of the Klein bottle
• Diagonal transformations of graphs and Dehn twists of surfaces
• Uniqueness and faithfulness of embedding of toroidal graphs
• Generating the triangulations of the projective plane
• Tight and untight triangulations of surfaces by complete graphs
• Diagonal transformations and cycle parities of quadrangulations on surfaces
• Wagner's theorem for torus graphs
• Diagonal transformations of triangulation on surfaces
• Bemerkungen zum Vierfarbenproblem
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• Diagonal flips in pseudo-triangulations on closed surfaces
• Triangulations on closed surfaces covered by vertices of given degree
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