Concepedia

Rainbow Numbers for Cycles in Plane Triangulations

Mirko Horňák, Stanislav Jendrol′, Ingo Schiermeyer, Roman Soták

Journal of Graph Theory · 2014 · 40 citations · 4 references

Concepts

Geometric ModelingRainbow NumbersDiscrete GeometryEngineeringGraph TheoryGeometryGeometric AlgorithmNatural SciencesGeometric Graph TheoryPlanar GraphLower BoundDelaunay TriangulationRainbow CyclesComputer-aided DesignUpper BoundDiscrete MathematicsComputational Geometry

Abstract

Abstract In the article, the existence of rainbow cycles in edge colored plane triangulations is studied. It is shown that the minimum number of colors that force the existence of a rainbow C 3 in any n ‐vertex plane triangulation is equal to . For a lower bound and for an upper bound of the number is determined.

References

4

Rainbow Generalizations of Ramsey Theory: A Survey

Shinya Fujita, Colton Magnant, Kenta Ozeki · Graphs and Combinatorics · 2010 · 188 citations

Graph Theory, Rainbow Generalizations, Combinatorial Design Theory +3

An Anti-Ramsey Theorem on Cycles

Juan José Montellano‐Ballesteros, V. Neumann‐Lara · Graphs and Combinatorics · 2005 · 94 citations

Graph Theory, Algebraic Graph Theory, Combinatorial Design +3

Rainbow Numbers for Cycles with Pendant Edges

Izolda Gorgol · Graphs and Combinatorics · 2008 · 17 citations

Rainbow Numbers, Optical Properties, Combinatorial Design Theory +2

Rainbow faces in edge‐colored plane graphs

Stanislav Jendrol′, J. Miškuf, Roman Soták et al. · Journal of Graph Theory · 2009 · 11 citations

Edge‐colored Plane Graphs, Geometric Graph Theory, Graph Theory +10