Richardson's theorem

The set of Richardson is a theorem of graph theory , one of the branches of mathematics . The set was designed by the American mathematician Moses Richardson in 1953 published . He deals with the question of the existence of kernels in finite directed graphs .

Formulation of the sentence

It can be summarized as follows:

Every finite directed graph without circles of odd length has at least one kernel.

literature

• Reinhard Diestel : Graph Theory (=  Graduate Texts in Mathematics . Volume 173 ). 3. Edition. Springer Verlag, Berlin / Heidelberg / New York 2005, ISBN 3-540-26182-6 ( MR2159259 ).
• Jørgen Bang-Jensen, Gregory Z. Gutin: Digraphs. Theory, Algorithms and Applications (=  Springer Monographs in Mathematics ). 2nd Edition. Springer Verlag , London / Dordrecht / Heidelberg / New York 2010, ISBN 978-1-84800-997-4 , doi : 10.1007 / 78-1-84800-998-1 . MR2472389
• Moses Richardson: Solutions of irreflexive relations . In: Annals of Mathematics (2) . tape 58/60 , 1953, pp. 573-590 ( MR0075184 ).
• Gunther Schmidt , Thomas Ströhlein: Relations and graphs (=  mathematics for computer scientists ). Springer Verlag, Berlin ( inter alia ) 1989, ISBN 3-540-50304-8 ( MR1011038 ).

References and footnotes

1. ^ Jørgen Bang-Jensen, Gregory Z. Gutin: Digraphs. 2010, pp. 119-120
2. ^ Reinhard Diestel: Graph Theory. 2005, p. 135
3. ^ Gunther Schmidt, Thomas Ströhlein: Relations and graphs. 1989, p. 188