Colloquia Mathematica Societatis János Bolyai
نویسندگان
چکیده
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 emergency calls .
منابع مشابه
Colloquia Mathematica Societatis Janos Bolyai 10. Infinite and Finite Sets, Keszthely (hungary), 1973 . on the Magnitude of Generalized Ramsey Numbers for Graphs S.a. Burr - P. Erdos
If G and H are graphs (which will mean finite, with no loops or parallel lines), define the Ramsey number r(G, H) to be the least number p such that if the lines of the complete graph Kp are colored red and blue (say), either the red subgraph contains a copy of G or the blue subgraph contains H. The diagonal Ranisei , numbers are given by r(G) _ = r(G, G) . These definitions follow those of C h...
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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...
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A hypergraphi is a collection of sets. This paper deals with finite hy-pergraphs only. The sets in the hypergraph are called edges, the elements of these edges are points. The degree of a point is the number of edges containing it. The hypergraph is r-uniform if every edge has r points. A hypergraph is simple if any two edges have at most one common point, and it is called a clique if any two e...
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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...
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I n Vol. 56, No. 11, of Notices, I saw a fascinating article with the title: Changing Faces—The Mistaken Portrait of Legendre. The author, Peter Duren, writes with understandable bewilderment: “It seems incredible that such egregious error could have gone undetected for somany years.” This encouraged me to publish, in the same journal, the story—no less fascinating—of the real face of János Bol...
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