Decomposition of a complete multigraph into simple paths: Nonbalanced handcuffed designs |
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| Authors: | Michael Tarsi |
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| Institution: | Department of Mathematics, University of California, Los Angeles, California 90024, USA |
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| Abstract: | The condition λv(v ? 1) ≡ 0 (mod 2m), v ? m + 1 is obviously necessary for the existence of an edge disjoint decomposition of a complete multigraph λKv into isomorphic simple paths consisting of m edges each. This condition is proved here to be sufficient. The proof is also valid in some cases when the given paths are not necessarity of the same length. |
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