ISSN 1234-3099 (print version)
ISSN 2083-5892 (electronic version)
SCImago Journal Rank (SJR) 2018: 0.763
Rejection Rate (2018-2019): c. 84%
Discussiones Mathematicae Graph Theory 26(2) (2006)
This is a problem by Michael Kubesa, Technical University Ostrava,
presented by Dalibor Froncek.
Let K2n be a complete graph and T a tree, both with 2n vertices.
A T-factorization of K2n is a collection of edge disjoint
spanning subgraphs (i.e., factors) T1,T2,... ,Tn of K2n, all
isomorphic to T. Every edge of K2n then appears in exactly one copy
M. Kubesa asked the following question: Suppose that there exists a
T-factorization of K2n. Is it then true that the vertex set of T
can be decomposed into two subsets, X and Y, such that
Notice that the sets X,Y in general are not the partite sets of
the bipartition of T.