The 7-cycle \(C_{7}\) is light in the family of planar graphs with minimum degree 5
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Publication:878637
DOI10.1016/j.disc.2005.11.080zbMath1115.05022OpenAlexW1970442864MaRDI QIDQ878637
Riste Škrekovski, Tomáš Madaras, Heinz-Juergen Voss
Publication date: 26 April 2007
Published in: Discrete Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.disc.2005.11.080
Related Items (17)
An analogue of Franklin's theorem ⋮ Unnamed Item ⋮ On the Decay of Crossing Numbers of Sparse Graphs ⋮ On the structure of essentially-highly-connected polyhedral graphs ⋮ On doubly light triangles in plane graphs ⋮ 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 ⋮ The vertex-face weight of edges in 3-polytopes ⋮ All tight descriptions of 3-stars in 3-polytopes with girth 5 ⋮ An improvement of Lebesgue's description of edges in 3-polytopes and faces in plane quadrangulations ⋮ Light graphs in families of polyhedral graphs with prescribed minimum degree, face size, edge and dual edge weight ⋮ On the weight of minor faces in triangle-free 3-polytopes ⋮ Low edges in 3-polytopes ⋮ Low minor faces in 3-polytopes ⋮ Each 3-polytope with minimum degree 5 has a 7-cycle with maximum degree at most 15
Cites Work
- On light cycles in plane triangulations
- Subgraphs with restricted degrees of their vertices in planar 3-connected graphs
- On \(3\)-connected plane graphs without triangular faces
- Light subgraphs of graphs embedded in the plane. A survey
- On vertex-degree restricted paths in polyhedral graphs
- On light subgraphs in plane graphs of minimum degree five
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