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Volume 19 - 1967

Contents

Page 7 of 7

Research Article

  • Cycles and Connectivity in Graphs

  • M. E. Watkins, D. M. Mesner
  • Published online by Cambridge University Press:
    20 November 2018, pp. 1319-1328
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  • In this note, G will denote a finite undirected graph without multiple edges, and V = V(G) will denote its vertex set. The largest integer n for which G is n-vertex connected is the vertex-connectivity of G and will be denoted by λ = λ(G). One defines ζ to be the largest integer z not exceeding |V| such that for any set U ⊂ V with |U| = z, there is a cycle in G which contains U. The symbol i(U) will denote the component index of U. As a standard reference for this and other terminology, the authors recommend O. Ore (3).

  • Lifting Inductive and Projective Limits

  • Johann Sonner
  • Published online by Cambridge University Press:
    20 November 2018, pp. 1329-1339
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  • In this paper, which is the fourth in a series of articles (11, 12, 13) on universal solutions in categories, a relationship between inductive limits and final structures (or projective limits and initial structures) is studied. The problems to be encountered are illustrated by the following example.

Page 7 of 7