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Homomorphisms in Graph Property Testing

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Topics in Discrete Mathematics

Part of the book series: Algorithms and Combinatorics ((AC,volume 26))

Abstract

Property-testers are fast randomized algorithms for distinguishing between graphs (and other combinatorial structures) satisfying a certain property, from those that are far from satisfying it. In many cases one can design property-testers whose running time is in fact independent of the size of the input. In this paper we survey some recent results on testing graph properties. A common thread in all the results surveyed is that they rely heavily on the simple yet useful notion of graph homomorphism. We mainly focus on the combinatorial aspects of property-testing.

Research supported in part by a USA Israeli BSF grant, by a grant from the Israel Science Foundation, and by the Hermann Minkowski Minerva Center for Geometry at Tel Aviv University.

Research supported in part by a Charles Clore Foundation Fellowship and an IBM Ph.D Fellowship.

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Author information

Authors and Affiliations

  1. Schools of Mathematics and Computer Science, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv, Israel

    Noga Alon

  2. School of Computer Science, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv, Israel

    Asaf Shapira

Authors
  1. Noga Alon
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  2. Asaf Shapira
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Editors and Affiliations

  1. Department of Applied Mathematics and Institute for Theoretical Computer Science ITI, Faculty of Mathematics and Physics, Charles University, Prague, Malostranské nám. 25, 118 00, Praha 1, Czech Republic

    Martin Klazar , Jan Kratochvíl , Martin Loebl , Jiří Matoušek  & Pavel Valtr , , ,  & 

  2. School of Mathematics, Georgia Institute of Technology, Atlanta, GA, 30332-0160, USA

    Robin Thomas

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Alon, N., Shapira, A. (2006). Homomorphisms in Graph Property Testing. In: Klazar, M., Kratochvíl, J., Loebl, M., Matoušek, J., Valtr, P., Thomas, R. (eds) Topics in Discrete Mathematics. Algorithms and Combinatorics, vol 26. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-33700-8_17

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