Property testing in bounded degree graphs
Oded Goldreich, Dana Ron · 1997
We further develop the study of testing graph properties as initiated by Goldreich, Goldwasser and Ron. Loosely speaking, given an oracle access to a graph, we wish to distinguish the case the graph has a pre-determined property from the case it is "far" from having this property. Whereas they view graphs as represented by their adjacency matrix and measure distance between graphs as a fraction of all possible vertex pairs, we view graphs as represented by bounded-length incidence lists and measure distance between graphs as a fraction of the maximum possible number of edges. Thus, while the previous model is most appropriate for the study of dense graphs, our model is most appropriate for the study of bounded-degree graphs. In particular,