7 research outputs found
Enclosings of Decompositions of Complete Multigraphs in -Edge-Connected -Factorizations
A decomposition of a multigraph is a partition of its edges into
subgraphs . It is called an -factorization if every
is -regular and spanning. If is a subgraph of , a
decomposition of is said to be enclosed in a decomposition of if, for
every , is a subgraph of .
Feghali and Johnson gave necessary and sufficient conditions for a given
decomposition of to be enclosed in some -edge-connected
-factorization of for some range of values for the parameters
, , , , : , and either ,
or and and , or and . We generalize
their result to every and . We also give some
sufficient conditions for enclosing a given decomposition of in
some -edge-connected -factorization of for every
and , where is a constant that depends only on ,
and~.Comment: 17 pages; fixed the proof of Theorem 1.4 and other minor change