Isomorphic factorizations VII. Regular graphs and tournaments

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It is shown using enumeration results that for r > 2t, almost all labeled r‐regular graphs cannot be factorized into t ⩾ 2 isomorphic subgraphs. However, no examples of such nonfactorizable graphs are known which satisfy the obvious divisibility condition that the number of edges is divisible by t. Similar observations hold for regular tournaments (t ⩾ 2} and for r‐regular digraphs (r > t ⩾ 2).

Original languageEnglish
Pages (from-to)117-122
Number of pages6
JournalJournal of Graph Theory
Issue number1
Publication statusPublished - 1984
Externally publishedYes

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