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Isomorphic path decompositions of crowns. (English) Zbl 1071.05563
The crown $$C_{n, k}$$ for positive integers $$n, k$$ is the graph with the vertex set $$\{a_1, \dots , a_n, b_1, \dots , b_n\}$$ whose edge set consists of edges $$a_i b_j$$, where $$1 \leq i \leq n$$ and $$j$$ is congruent modulo $$n$$ to an integer between $$i$$ and $$i + k - 1$$. The decomposition of a crown $$C_{n, k}$$ into paths $$P_l$$ of length $$l$$ for given positive integers $$n, k, l$$ is studied. The main theorem states a necessary and sufficient condition for the existence of such a decomposition.

##### MSC:
 05C70 Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.)