We extend the bounded degree graph model for property testing introduced by Goldreich and Ron (Algorithmica, 2002) to hypergraphs. In this framework, we analyse the query complexity of three fundamental hypergraph properties: colorability, $k$-partiteness, and independence number. We present a randomized algorithm for testing $k$-partiteness within families of $k$-uniform $n$-vertex hypergraphs of bounded treewidth whose query complexity does not depend on $n$. In addition, we prove optimal lower bounds of $\Omega(n)$ on the query complexity of testing algorithms for $k$-colorability, $k$-partiteness, and independence number in $k$-uniform $n$-vertex hypergraphs of bounded degree. For each of these properties, we consider the problem of explicitly constructing $k$-uniform hypergraphs of bounded degree that differ in $\Theta(n)$ hyperedges from any hypergraph satisfying the property, but where violations of the latter cannot be detected in any neighborhood of $o(n)$ vertices.

翻译：我们将Goldreich和Ron（Algorithmica，2002）提出的有界度图模型的性质测试框架扩展至超图。在此框架下，我们分析了三个基本超图性质的查询复杂度：可着色性、$k$-部性与独立数。我们提出了一种随机算法，用于测试具有有界树宽的$k$-一致$n$顶点超图族中的$k$-部性，其查询复杂度不依赖于$n$。此外，我们证明了在有界度的$k$-一致$n$顶点超图中，测试$k$-可着色性、$k$-部性与独立数的算法的查询复杂度具有$\Omega(n)$的最优下界。针对这些性质中的每一个，我们考虑了显式构造有界度$k$-一致超图的问题，这些超图与满足该性质的任何超图相差$\Theta(n)$条超边，但违反该性质的情况无法在$o(n)$个顶点的任何邻域中被检测到。