We derive a sufficient condition for a sparse graph G on n vertices to contain a copy of a tree T of maximum degree at most d on (1 − )n vertices, in terms of the expansion prop...
We show that in the bounded degree model for graph property testing, adaptivity is essential. An algorithm is non-adaptive if it makes all queries to the input before receiving an...
We present a sublinear-time algorithm for testing whether a bounded degree graph is bipartite or far from being bipartite. Graphs are represented by incidence lists of bounded len...
We consider the problem of testing 3-colorability in the bounded-degree model. We show that, for small enough ε, every tester for 3colorability must have query complexity Ω(n)....
We study restricted homomorphism dualities in the context of classes with bounded expansion. This presents a generalization of restricted dualities obtained earlier for bounded deg...