2002 | OriginalPaper | Chapter
The Structural Decomposition
Authors : Michael Molloy, Bruce Reed
Published in: Graph Colouring and the Probabilistic Method
Publisher: Springer Berlin Heidelberg
Included in: Professional Book Archive
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In this chapter we will obtain a decomposition theorem for general graphs similar to that obtained in Chap. 11 for minimal counterexamples to the Beutelspacher-Hering Conjecture. That is, we will partition V (G) into sets D1,..., D ι and S where the D i are “dense clique-like” sets and all the vertices in S are sparse.