Abstract
In this paper we initiate the study of testing properties of hypergraphs. The goal of property testing is to distinguish between the case whether a given object has a certain property or is “far away” from the property. We prove that the fundamental problem of ℓ-colorability of k-uniform hypergraphs can be tested in time independent of the size of the hypergraph. We present a testing algorithm that examines only (k l/∈ o(k) entries of the adjacency matrix of the input hypergraph, where ∈ is a distance parameter independent of the size of the hypergraph. Notice that this algorithm tests only a constant number of entries in the adjacency matrix provided that ℓ, k, and ∈ are constant.
Research supported in part by an SBR grant No. 421090 and DFG grant Me872/7-1.
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Czumaj, A., Sohler, C. (2001). Testing Hypergraph Coloring. In: Orejas, F., Spirakis, P.G., van Leeuwen, J. (eds) Automata, Languages and Programming. ICALP 2001. Lecture Notes in Computer Science, vol 2076. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48224-5_41
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DOI: https://doi.org/10.1007/3-540-48224-5_41
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