Elsevier

Discrete Mathematics

Volume 8, Issue 1, March 1974, Pages 41-47
Discrete Mathematics

A factorization theorem for a certain class of graphs

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Abstract

In this note we give a necessary and sufficient condition for factorization of graphs satisfying the “odd cycle property”. We show that a graph G with the odd cycle property contains a [ki] factor if and only if the sequence [H]+[ki] is graphical for all subgraphs H of the complement of G.

A similar theorem is shown to be true for all digraphs.

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The content of this note is taken from the author's Ph.D. Thesis, Department of Mathematics, University of California, Berkeley. Research supported in part by the Air Force Office of Scientific Research Grant AFOSR-71-2076.

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Present address Computer Science Department, University of Texas at Austin, Austin, Texas 78712, USA.