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Nearly Planar Graphs and {\lambda}-flat Graphs

Grigoriev, Alexander ; Koutsonas, Athanassios ; Thilikos, Dimitrios M Thilikos, Dimitrios M (Editor)

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  • Título:
    Nearly Planar Graphs and {\lambda}-flat Graphs
  • Autor: Grigoriev, Alexander ; Koutsonas, Athanassios ; Thilikos, Dimitrios M
  • Thilikos, Dimitrios M (Editor)
  • Assuntos: Mathematics ; Combinatorics ; Mathematics
  • Descrição: A graph G is {\xi}-nearly planar if it can be embedded in the sphere so that each of its edges is crossed at most {\xi} times. The family of {\xi}-nearly planar graphs is widely extending the notion of planarity. We introduce an alternative parameterized graph family extending the notion of planarity, the {\lambda}-flat graphs, this time defined as powers of plane graphs in regard to a novel notion of distance, the wall-by-wall distance. We show that the two parameterized graph classes are parametrically equivalent.
  • Idioma: Inglês

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