Centenary of <i>Acta Societatis Botanicorum Poloniae</i>

Colloquia Mathematica Societatis

For any infinite cardinal K define a family .F of sets to be a Kalmost-disjoint family (K-ADF) iff U y has cardinality K, each member of .F has cardinality K, and the intersection of any two distinct members of F has cardinality strictly less than K . Define such a family to be a K-maximal almost-disjoint family (K-MADF) iff for every set S c U 'F of cardinality K there exists a set FEE JF* who...

Colloquia Mathematica Societatis Janos Bolyai

The authors continue their study of extremal problems of Turán type for directed graphs with multiple edges, now permitting any finite nonnegative integer multiplicity . Having proved earlier (for the case of multiplicity at most 1) that there exists, for any family of "sample" digraphs, a matrix which represents the structure of an "asymptotically extremal sequence" of digraphs (containing non...

Colloquia Mathematica Societatis János Bolyai

1 . Our investigations might be suggested by a sort of optimalization problem which could be described vividly in practical terms as follows : suppose we are given a network of routes on which there are critical points endangered by fire. We want to place fire stations at an appropriate number of points from which any endangered point can be reached within a given time interval in case of emerg...

Colloquia Mathematica Societatis János Bolyai

For a given finite graph G and positive integer k, let r(G ; k) denote the least integer r such that if the edges of Kr , the complete graph on r vertices, are arbitrarily partitioned into k classes then some class contains a subgraph isomorphic to G . The existence of r(G ; k) follows at once from the well-known theorem of R a m s e y {8] which asserts that r(Kn ; k) < for all n and k . In thi...

The Centenary of Radiology