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Even-hole-free graphs. I: Decomposition theorem. (English) Zbl 1005.05034
Summary: We prove a decomposition theorem for even-hole-free graphs. The decompositions used are 2-joins and star, double-star and triple-star cutsets. This theorem is used in the second part of this paper to obtain a polytime recognition algorithm for even-hole-free graphs.

##### MSC:
 05C70 Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.) 05C17 Perfect graphs 05C85 Graph algorithms (graph-theoretic aspects)
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