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{\bf Zsolt Fekete and J\'acint Szab\'o}
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{\bf Equitable Partitions to Spanning Trees in a Graph}
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In this paper we first prove that if the edge set of an undirected
graph is the disjoint union of two of its spanning trees, then for
every subset $P$ of edges there exists a spanning tree decomposition
that cuts $P$ into two (almost) equal parts. The main result of the
paper is a further extension of this claim: If the edge set of a graph
is the disjoint union of two of its spanning trees, then for every
stable set of vertices of size 3, there exists such a spanning tree
decomposition that cuts the stars of these vertices into (almost)
equal parts. This result fails for 4 instead of 3. The proofs are elementary.
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