Konig's Lemma

Konig's Lemma

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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. K nig's lemma or K nig's infinity lemma is a theorem in graph theory due to D nes K nig (1936). It gives a sufficient condition for an infinite graph to have an infinitely long path. The computability aspects of this theorem have been thoroughly investigated by researchers in mathematical logic, especially in computability theory. This theorem also has important roles in constructive mathematics and proof theory. Note that, although K nig's name is properly spelled with a double acute accent, the lemma named after him is customarily spelled with an umlaut. If G is a connected graph with infinitely many vertices such that every vertex has finite degree (that is, each vertex is adjacent to only finitely many other vertices) then G contains an infinitely long simple path, that is, a path with no repeated vertices. A common special case of this is that every tree that contains infinitely many vertices, each having finite degree, has at least one infinite simple path. Note that the vertex degrees must be finite, but need not be bounded: it is possible to have one vertex of degree 10, another of degree 100, a third of degree 1000, and so on.show more

Product details

  • Paperback | 76 pages
  • 152 x 229 x 5mm | 122g
  • Culp Press
  • Saarbrucken, Germany
  • English
  • black & white illustrations
  • 6136774453
  • 9786136774459