Theorie der endlichen und unendlichen Graphen. Kombinatorische Topologie der Streckenkomplexe. (German) Zbl 0013.22803

König, Dénes

Mathematik und ihre Anwendung in Monographien und Lehrbüchern. 16. Leipzig: Akademische Verlagsgesellschaft mbH. xi, 258 S., 107 Fig. (1936).

A thorough monograph, containing much classical information, with extensions by the author – particularly to infinite graphs. Many interesting applications to puzzles, games, and abstract sets, but little attempt to reconcile concepts and terms with those used in the modern theory of \(n\)-complexes.
Summary by chapters: fundamental notions of graphs (1); unicursal (2) and labyrinth (3) problems; trees (4,5); questions special to infinite graphs (6); bases for vertices and edges of oriented graphs (7); applications to logic, games of position, e. g. chess, and group diagrams (8); linear forms in edges [= 1-chains], cycles, starforms [= duals of bounding cycles] (9), and the same mod 2 (10); factorization (11), particularly graphs of third degree with their relation to four-color problem (12), and extensions to infinite graphs (13); questions of separation, applications to determinants (14). Copious references to sources; good bibliography.

Reviewer: A. W. Tucker (Princeton)

MSC:

05-01	Introductory exposition (textbooks, tutorial papers, etc.) pertaining to combinatorics
05Cxx	Graph theory
57-01	Introductory exposition (textbooks, tutorial papers, etc.) pertaining to manifolds and cell complexes

Keywords:

finite graphs; infinite graphs; combinatorial topology; line complexes