论文信息 - A Problem of Ulam on Planar Graphs

A Problem of Ulam on Planar Graphs

The following problem was raised by S. M. Ulam: Does there exist a countable planar graph Go such that every countable planar graph is isomorphic to a subgraph of G 0 ? We answer this question in the negative.

János Pach

[1] J. Spencer. Probabilistic Methods in Combinatorics , 1974 .

[2] R. Rado. A SEMINAR ON GRAPH THEORY , 1969 .

[3] R. Rado. Universal graphs and universal functions , 1964 .

[4] János Pach. On metric properties of countable graphs , 1977 .

[5] Bjarni Jónsson,et al. Homogeneous Universal Relational Systems. , 1960 .

[6] B. Rotman,et al. Remarks on Some Theorems of Rado on Universal Graphs , 1971 .

[7] Saharon Shelah,et al. Notes on combinatorial set theory , 1973 .

[8] Claude Berge,et al. Graphs and Hypergraphs , 2021, Clustering.