an:04185636
Zbl 0719.05033
Robertson, Neil; Seymour, P. D.
Graph minors. VIII: A Kuratowski theorem for general surfaces
EN
J. Comb. Theory, Ser. B 48, No. 2, 255-288 (1990).
0095-8956
1990
j
05C10
graph embedding; surface with boundary; Wagner's conjecture; bounded genus; minor
[Part VII, cf. ibid. 45, No.2, 212-254 (1988; Zbl 0658.05044).]
In their eighth papers of a long series of papers towards a proof of Wagner's conjecture, the authors settle the case of graphs of bounded genus. Hence, for any infinite set of graphs of bounded genus, some member of the set is isomorphic to a minor of another. As a consequence, for every closed surface the list of forbidden subgraphs which characterizes the embeddability in that surface is finite. This answers a question of P. Erdős raised as early as in the 1930's.
J.Širáň (Bratislava)
0658.05044