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Displaying similar documents to “Unavoidable set of face types for planar maps”

Bicubic planar maps

William T. Tutte (1999)

Annales de l'institut Fourier

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A numerical function of bicubic planar maps found by the author and colleagues is a special case of a polynomial due to François Jaeger.

Planar Ramsey numbers

Izolda Gorgol (2005)

Discussiones Mathematicae Graph Theory

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The planar Ramsey number PR(G,H) is defined as the smallest integer n for which any 2-colouring of edges of Kₙ with red and blue, where red edges induce a planar graph, leads to either a red copy of G, or a blue H. In this note we study the weak induced version of the planar Ramsey number in the case when the second graph is complete.

Light edges in 1-planar graphs with prescribed minimum degree

Dávid Hudák, Peter Šugerek (2012)

Discussiones Mathematicae Graph Theory

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A graph is called 1-planar if it can be drawn in the plane so that each edge is crossed by at most one other edge. We prove that each 1-planar graph of minimum degree δ ≥ 4 contains an edge with degrees of its endvertices of type (4, ≤ 13) or (5, ≤ 9) or (6, ≤ 8) or (7,7). We also show that for δ ≥ 5 these bounds are best possible and that the list of edges is minimal (in the sense that, for each of the considered edge types there are 1-planar graphs whose set of types of edges contains...