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Cycle decompositions of complete multigraphs
Author(s) -
Smith Benjamin R.
Publication year - 2010
Publication title -
journal of combinatorial designs
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.618
H-Index - 34
eISSN - 1520-6610
pISSN - 1063-8539
DOI - 10.1002/jcd.20229
Subject(s) - multigraph , corollary , digraph , mathematics , combinatorics , prime (order theory) , discrete mathematics , graph
In this paper we establish necessary and sufficient conditions for decomposing the complete multigraph λ K n into cycles of length λ, and the λ‐fold complete symmetric digraph λ K * ninto directed cycles of length λ. As a corollary to these results we obtain necessary and sufficient conditions for decomposing λ K n (respectively, λ K * n ) into cycles (respectively, directed cycles) of prime length. © 2009 Wiley Periodicals, Inc. J Combin Designs 18: 85–93, 2010