### The characterization of the cut of funnel in a planar semidynamical system

Krzysztof Ciesielski (1990)

Annales Polonici Mathematici

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Krzysztof Ciesielski (1990)

Annales Polonici Mathematici

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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.

D.G. Kirkpatrick (1988)

Discrete & computational geometry

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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.

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...

Brandes, Ulrik, Handke, Dagmar (1998)

Discrete Mathematics and Theoretical Computer Science. DMTCS [electronic only]

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Bojan Mohar (1992)

Mathematica Slovaca

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Felsner, Stefan, Zickfeld, Florian (2008)

The Electronic Journal of Combinatorics [electronic only]

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Robert E. Tarjan, P. Rosenstiehl (1986)

Discrete & computational geometry

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de Fraysseix, Hubert, Ossona de Mendez, Patrice (2001)

Journal of Graph Algorithms and Applications

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