Publication: El teorema de Jordan y los grados planares
Loading...
Official URL
Full text at PDC
Publication Date
2016-06
Authors
Advisors (or tutors)
Editors
Journal Title
Journal ISSN
Volume Title
Publisher
Citations
Exportar
Abstract
En este trabajo estudiamos el teorema de la curva de Jordan, con énfasis especial en algunos aspectos relacionados con la Teoría de Grafos, más exactamente con la planaridad. Explicamos como los dos famosos ejemplos K5 y K3,3 de no planaridad contienen una parte relevante de la esencia topológica del teorema de Jordan. Además, analizamos cuidadosamente las construcciones a menudo imprecisas escondidas en la demostración del teorema de Kuratowski, proporcionando pruebas rigurosas de algunos hechos que usualmente se dan por inmediatos
In this work we study the Jordan Curve Theorem, with special emphasis on some aspects connected with Graph Theory, namely planarity. We explain how the famous non-planar graph examples K5 and K3,3 contain a relevant part of the topological essence of the Jordan Theorem. Also, we discuss carefully the usually understated constructions behind the proof of Kuratowski Theorem, providing rigurous proofs for some facts that are usually taken for granted.
In this work we study the Jordan Curve Theorem, with special emphasis on some aspects connected with Graph Theory, namely planarity. We explain how the famous non-planar graph examples K5 and K3,3 contain a relevant part of the topological essence of the Jordan Theorem. Also, we discuss carefully the usually understated constructions behind the proof of Kuratowski Theorem, providing rigurous proofs for some facts that are usually taken for granted.
Description
UCM subjects
Unesco subjects
Keywords
Citation
[1] R. Diestel: Graph Theory. Springer-Verlag Berlin Heidelberg, 2005.
[2] S. Herke: Planar Graphs. https://www.youtube.com/watch?v=wnYtITkWAYA
[3] R. Luisto: Proof of the Jordan Curve Theorem. http://www.helsinki.fi/˜luisto/JordanCurveTheorem.pdf
[4] J. Margalef, E. Outerelo: Introducción a la Topología. Editorial Complutense, 1993.
[5] B. Mohar, C. Thomassen: Graphs on surfaces. McGraw Hill, Madrid 2004.
[6] V. Munoz, J. J. Madrigal: Topología Algebraica. Sanz y Torres, Madrid 2015.
[7] M. H. A. Newman: Elements of the topology of plane sets of points. University Press, Cambridge, 1964.
[8] E. Outerelo, J. M. Sanchez: Elementos de Topología. Sanz y Torres, Madrid 2008.
[9] K. H. Rosen: Matem´atica discreta y sus aplicaciones. McGraw Hill, Madrid 2004.
[10] A. Sheffer: Kuratowski’s Theorem. http://www.math.caltech.edu/˜2014-15/2term/ma006b/10%20Planar3.pdf
[11] J. Tantalo: Planarity. http://planarity.net
[12] C. Thomassen: The Jordan-Sch¨onflies Theorem and the Classification of surfaces. http://www.maths.ed.ac.uk/˜aar/jordan/thomass.pdf