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Isomorphic factorizations VII. Regular graphs and tournaments
Author(s) -
Wormald N. C.
Publication year - 1984
Publication title -
journal of graph theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 54
eISSN - 1097-0118
pISSN - 0364-9024
DOI - 10.1002/jgt.3190080114
Subject(s) - mathematics , combinatorics , divisibility rule , enumeration , discrete mathematics
Abstract It is shown using enumeration results that for r > 2 t , 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).