# zbMATH — the first resource for mathematics

A short proof of Halin’s grid theorem. (English) Zbl 1062.05138
An end of an infinite graph is an equivalence class of rays (1-way infinite paths), where two rays are equivalent if no finite set of vertices separates them. An end is thick if there are infinitely many disjoint rays all converging to that end. In the paper there is a short proof of a theorem by Halin, which states that whenever a graph has a thick end, it has a subgraph isomorphic to a subdivision of a hexagonal grid $$H$$ whose rays all belong to that end.

##### MSC:
 05C99 Graph theory 05C83 Graph minors
##### Keywords:
hexagonal grid; infinite graph; ray; thick end
Full Text:
##### References:
 [1] R. Diestel,Graph Theory. Springer-Verlag, 2000, 2nd edition. http ://www.math.uni-hamburg.de/home/diestel/books/graph.theory/download.html [2] R. Diestel andD. Kühn, Graph-theoretical versus topological ends of graphs.J. Comb. Theory B 87 (2003), 197–206. · Zbl 1035.05031 · doi:10.1016/S0095-8956(02)00034-5 [3] R. Halin, Über unendliche Wege in Graphen.Math. Ann 157 (1964), 125–137. · Zbl 0125.11701 · doi:10.1007/BF01362670 [4] R. Halin, Über die Maximalzahl fremder unendlicher Wege in Graphen.Math. Nachr. 30 (1965), 63–85. · Zbl 0131.20904 · doi:10.1002/mana.19650300106
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.