Testing Hereditary Properties of Non-Expanding Bounded-Degree Graphs

We study graph properties which are testable for bounded degree graphs in time independent of the input size. Our goal is to distinguish between graphs having a predetermined graph property and graphs that are far from every graph having that property. It is believed that almost all, even very simple graph properties require a large complexity to be tested for arbitrary (bounded degree) graphs. Therefore in this paper we focus our attention on testing graph properties for special classes of graphs. We call a graph family non-expanding if every graph in this family has a weak expansion (its expansion is O(1/ log2 n), where n is the graph size). A graph family is hereditary if it is closed under vertex removal. Similarly, a graph property is hereditary if it is closed under vertex removal. We call a graph property Π to be testable for a graph family F if for every graph G ∈ F, in time independent of the size of G we can distinguish between the case when G satisfies property Π and w...

• Type: Journal
• Year: 2007
• Where: ECCC
• Authors: Artur Czumaj, Asaf Shapira, Christian Sohler
• Keywords: Degree Graphs, ECCC 2007, Graph Properties, Graph Property