We consider some classes of non-necessarily continuous functions which have played a role in a recent literature on optimization and non-cooperative game theory. With respect to the uniform convergence metric, we prove that the limit of a converging sequence of weakly pseudocontinuous functions is weakly pseudocontinuous, but the similar property is not verified for functions which are either t...

A hereditary graph property is a collection of labeled graphs, closed under isomorphism and also under the taking of induced subgraphs. Its speed is the number of graphs in the property as a function of the number of vertices in the graph. Earlier research has characterized the speeds for hereditary graph properties up to n(1+o(1))n, and described the properties that have those smaller speeds. ...

We consider natural graph property tests, which act entirely independently of the size of the graph being tested (not just having a number of queries independent of the size). We introduce the notion of graph properties being inflatable — closed under taking (balanced) blowups — and show that the query complexity of natural tests for a property are related to the degree to which it is approxima...

For a property π on graphs, the edge-contraction problem with respect to π is defined as a problem of finding a set of edges of minimum cardinality whose contraction results in a graph satisfying the property π. This paper gives a lower bound for the approximation ratio for the problem for any property π that is hereditary on contractions and determined by biconnected components. key words: edg...

A Banach space E has the Grothendieck property if every (linear bounded) operator from E into c0 is weakly compact. It is proved that, for an integer k > 1, every k-homogeneous polynomial from E into c0 is weakly compact if and only if the space P(kE) of scalar valued polynomials on E is reflexive. This is equivalent to the symmetric k-fold projective tensor product of E (i.e., the predual of P...

We show that a strong form of the so called Lindström’s Theorem [4] fails to generalize to extensions of Lκω and Lκκ: For weakly compact κ there is no strongest extension of Lκω with the (κ, κ)compactness property and the Löwenheim-Skolem theorem down to κ. With an additional set-theoretic assumption, there is no strongest extension of Lκκ with the (κ, κ)-compactness property and the LöwenheimS...

An additive hereditary property of graphs is a class of simple graphs which is closed under unions, subgraphs and isomorphisms. Let P and Q be hereditary properties of graphs. The generalized edge-chromatic number ρQ(P) is defined as the least integer n such that P ⊆ nQ. We investigate the generalized edge-chromatic numbers of the properties → H, Ik, Ok, W∗ k , Sk and Dk.

The hereditary property of hypergraphs generated by the cost colouring notion is considered in the paper. First, we characterize all maximal graphs with respect to this property. Second, we give the generating function for the sequence describing the number of such graphs with the numbered order. Finally, we construct a maximal hypergraph for each admissible number of vertices showing some dens...