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Flipping Triangles and Rectangles

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Book cover Computing and Combinatorics (COCOON 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6842))

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Abstract

We study the chromatic number of the flip graph of triangles determined by n points in convex position in the plane, and present new or improved bounds on several related parameters for this graph. We also find the chromatic numbers of two related graphs: the rectangle flip graph which generalizes the shift graph, and the rolling block graph from the popular puzzle “Rolling Block Maze.”

Supported in part by NSF grant DBI-0743670.

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References

  1. Abbott, R.: Rolling-block mazes, Website at http://www.logicmazes.com/rb/column.html

  2. Buchin, K., Buchin, M., Demaine, E.D., Demaine, M.L., El-Khechen, D., Fekete, S.P., Knauer, C., Schulz, A., Taslakian, P.: On rolling cube puzzles. In: Proceedings of the 19th Canadian Conference on Computational Geometry (CCCG 2007), pp. 141–144 (2007)

    Google Scholar 

  3. Dumitrescu, A., Jiang, M.: Coloring translates and homothets of a convex body. Beiträge zur Algebra und Geometrie, doi:10.1007/s13366-011-0048-4

    Google Scholar 

  4. Erdős, P., Hajnal, A.: On chromatic number of infinite graphs. In: Proceedings of the Colloquium on Theory of Graphs held at Tihany, Hungary, September 1966, pp. 83–98. Academic Press, New York (1968)

    Google Scholar 

  5. Fabila-Monroy, R., Flores-Peñaloza, D., Huemer, C., Hurtado, F., Urrutia, J., Wood, D.R.: On the chromatic number of some flip graphs. Discrete Mathematics and Theoretical Computer Science 11, 47–56 (2009)

    MathSciNet  MATH  Google Scholar 

  6. Flaxman, A.D., Hoory, S.: Maximum matchings in regular graphs of high girth. Electronic Journal of Combinatorics 14, #N1 (2007)

    MathSciNet  MATH  Google Scholar 

  7. Friedman, E.: Rolling block mazes, Website at http://www2.stetson.edu/~efriedma/rolling/

  8. Gerke, S., McDiarmid, C.: Graph imperfection. Journal of Combinatorial Theory, Series B 83, 58–78 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  9. Harner, C.C., Entringer, R.C.: Arc colorings of digraphs. Journal of Combinatorial Theory, Series B 13, 219–225 (1972)

    Article  MathSciNet  MATH  Google Scholar 

  10. Scheinerman, E.R., Ullman, D.H.: Fractional Graph Theory: A Rational Approach to the Theory of Graphs. John Wiley & Sons, Chichester (1997)

    MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Computer Science, Utah State University, Logan, UT, 84322-4205, USA

    Minghui Jiang

Authors
  1. Minghui Jiang
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Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Texas-Pan American, 78539, Edinburg, TX, USA

    Bin Fu

  2. Department of Computer Science, University of Texas at Dallas, 75080, Richardson, TX, USA

    Ding-Zhu Du

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© 2011 Springer-Verlag Berlin Heidelberg

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Jiang, M. (2011). Flipping Triangles and Rectangles. In: Fu, B., Du, DZ. (eds) Computing and Combinatorics. COCOON 2011. Lecture Notes in Computer Science, vol 6842. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22685-4_47

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  • DOI: https://doi.org/10.1007/978-3-642-22685-4_47

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-22684-7

  • Online ISBN: 978-3-642-22685-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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