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....

A property of graphs is any class of graphs closed under isomorphism. Let P1,P2, . . . ,Pn be properties of graphs. A graph G is (P1,P2, . . . ,Pn)-partitionable if the vertex set V (G) can be partitioned into n sets, {V1, V2, . . . , Vn}, such that for each i = 1, 2, . . . , n, the graph G[Vi] ∈ Pi. We write P1◦P2◦ · · · ◦Pn for the property of all graphs which have a (P1,P2, . . . ,Pn)-partit...

A characteristic algebra for a hereditary property of identities of a fixed type τ is an algebra A such that for any variety V of type τ , we have A ∈ V if and only if every identity satisfied by V has the property p. This is equivalent to A being a generator for the variety determined by all identities of type τ which have property p. PÃlonka has produced minimal (smallest cardinality) charact...

This thesis deals mainly with hereditary coreflective subcategories of the category Top of topological spaces. After preparing the basic tools used in the rest of thesis we start by a question which coreflective subcategories of Top have the property SA = Top (i.e., every topological space can be embedded in a space from A). We characterize such classes by finding generators of the smallest cor...

Let H be a fixed finite graph and let → H be a hom-property, i.e. the set of all graphs admitting a homomorphism into H . We extend the definition of → H to include certain infinite graphs H and then describe the minimal reducible bounds for → H in the lattice of additive hereditary properties and in the lattice of hereditary properties.

We show that if X is a tight subspace of C(K) then X has the Pe lczyński property and X is weakly sequentially complete. We apply this result to the space U of uniformly convergent Taylor series on the unit circle and using a minimal amount of Fourier theory prove that U has the Pe lczyński property and U is weakly sequentially complete. Using separate methods, we prove U and U have the Dunford...

We show that Meyniel weakly triangulated graphs are co-perfectly orderable (equivalently , that P 5-free weakly triangulated graphs are perfectly orderable). Our proof is algorithmic, and relies on a notion concerning separating sets, a property of weakly triangulated graphs, and several properties of Meyniel weakly triangulated graphs.

Distance-hereditary graphs are in important graph class theory, as they well-placed the hierarchy and permit many algorithmic results. We investigate structural advantages of a directed version this well-researched class. Since previously defined distance-hereditary digraphs do not recursive structure, we define twin-distance-hereditary graphs, which can be constructed by several twin pendant v...

In this Letter, we consider the parameterized complexity of the following problem: Given a hereditary property P on digraphs, an input digraph D and a positive integer k, does D have an induced subdigraph on k vertices with property P? We completely characterize hereditary properties for which this induced subgraph problem is W [1]-complete for two classes of directed graphs: general directed g...

For a graph property X, let Xn be the number of graphs with vertex set {1, . . . , n} having property X, also known as the speed of X. A property X is called factorial if X is hereditary (i.e. closed under taking induced subgraphs) and n1 ≤ Xn ≤ n2 for some positive constants c1 and c2. Hereditary properties with the speed slower than factorial are surprisingly well structured. The situation wi...