Geodesic
Equitable partitions to spanning trees in a graph
The electronic journal of combinatorics, Tome 18 (2011) no. 1
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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.
DOI : 10.37236/708
Classification : 05C70, 05B35, 05C05
Mots-clés : disjoint spanning trees, base partitions of matroids 
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     author = {Zsolt Fekete and J\'acint Szab\'o},
     title = {Equitable partitions to spanning trees in a graph},
     journal = {The electronic journal of combinatorics},
     year = {2011},
     volume = {18},
     number = {1},
     doi = {10.37236/708},
     zbl = {1243.05196},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/708/}
}
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Zsolt Fekete; Jácint Szabó. Equitable partitions to spanning trees in a graph. The electronic journal of combinatorics, Tome 18 (2011) no. 1. doi: 10.37236/708

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