Lajos Soukup
We investigate the relationship between some theorems in finite combinatorics and their infinite counterparts: given a ``finite'' result how one can get an ``infinite'' version of it? We will also analyze the relationship between the proofs of a ``finite'' theorem and the proof of its ``infinite'' version.
Besides these comparisons, the paper gives a proof of a theorem of Erdös, Grünwald and Vázsonyi giving the full descriptions of graphs having one/two-way infinite Euler lines. The last section contains some new results: an infinite version of a multiway-cut theorem is included.
Key words and phrases: graphs, infinite, infinite Euler trail, Euler's theorem, König's theorem, Menger's theorem, Hall's theorem, infinite digraphs, multiway-cut, elementary submodel, Gödel's compactness theorem
2000 Mathematics Subject Classification: 05E99
Downloading the paper