Authors: Dress, Andreas
Stevanović, Dragan 
Title: A note on a theorem of Horst Sachs
Journal: Annals of Combinatorics
Volume: 8
Issue: 4
First page: 487
Last page: 497
Issue Date: 1-Jan-2005
ISSN: 0218-0006
DOI: 10.1007/s00026-004-0235-1
Abstract: 
In this note, we present an apparently new and rather short proof of a celebrated theorem of Horst Sachs characterizing bipartite finite graphs in term of their eigenvalue spectrum. Moreover, the simplicity of the proof allows us to establish this theorem and related results as a special instance of much more general assertions regarding the spectral theory of "compact graphs". Finally, some intriguing possible generalizations to locally finite, yet not "compact" graphs suggested by Horst Sachs are discussed in the last section.
Keywords: Bipartite graphs | Compact graphs | Eigenvalues of graphs | Harmonic graphs | Locally finite graphs | Semiharmonic graphs
Publisher: Springer Link
Project: Serbian Ministry of Science, Technology and Development, Grant 1227

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