We provide a forbidden induced subsystem characterization of those independence systems which are matroids. On this basis we describe a method for characterizing classes of matroid-deening graphs, associated to every hereditary graph property.

The well-known Rado graph R is universal in the set of all countable graphs I, since every countable graph is an induced subgraph of R. We study universality in I and, using R, show the existence of 20 pairwise non-isomorphic graphs which are universal in I and denumerably many other universal graphs in I with prescribed attributes. Then we contrast universality for and universality in induced-...

A graph is clique-Helly when its cliques satisfy the Helly property. A graph is hereditary clique-Helly when every induced subgraph of it is clique-Helly. The decision problems associated to the stability, chromatic, clique and clique-covering numbers are NP-complete for clique-Helly graphs. In this note, we analyze the complexity of these problems for hereditary clique-Helly graphs. Some of th...

This article provides a general statement and technique for solving the problem of oscillations hereditarily deformable aircraft in gas flow with finite number degrees freedom. Using Lagrange equations variational principle hereditary theory viscoelasticity, motion under consideration are derived. The generalized forces acting on subsonic flight mode determined according to stationarity hypothe...

If P is a hereditary property then we show that, for the existence of a perfect f -factor, P is a sufficient condition for countable graphs and yields a sufficient condition for graphs of size א1. Further we give two examples of a hereditary property which is even necessary for the existence of a perfect f -factor. We also discuss the א2-case. We consider graphs G = (V,E), where V = V (G) is a ...

The product P◦Q of graph properties P,Q is a class of all graphs having a vertex-partition into two parts inducing subgraphs with properties P and Q, respectively. For a graph invariant φ and a graph property P we define φ(P) as the minimum of φ(F ) taken over all minimal forbidden subgraphs F of P . An invariant of graph properties φ is said to be additive with respect to reducible hereditary ...

It is shown that the tensor product JH⊗̃ǫJH fails Pe lczńyski’s property (u). The proof uses a result of Kwapień and Pe lczńyski on the main triangle projection in matrix spaces. The Banach space JH constructed by Hagler [1] has a number of interesting properties. For instance, it is known that JH contains no isomorph of l, and has property (S): every normalized weakly null sequence has a subseq...

For a graph property P, the edit distance of a graph G from P, denoted EP(G), is the minimum number of edge modifications (additions or deletions) one needs to apply to G in order to turn it into a graph satisfying P. What is the furthest graph on n vertices from P and what is the largest possible edit distance from P? Denote this maximal distance by ed(n,P). This question is motivated by algor...

Let G be an algebraic group over an algebraically closed field, acting on a variety X with finitely many orbits. Staggered sheaves are certain complexes of G-equivariant coherent sheaves on X that seem to possess many remarkable properties. In this paper, we construct “standard” and “costandard” objects in the category of staggered sheaves, and we prove that that category has enough projectives...