Abstract
We prove that every connected graph can be edge-decomposed into a spanning tree, an even graph, and a star forest.
Highlights
All graphs in this paper are simple and finite
We prove that every connected graph can be edge-decomposed into a spanning tree, an even graph, and a star forest
A decomposition of a graph G is a collection of edge-disjoint subgraphs whose union is G
Summary
All graphs in this paper are simple and finite. A decomposition of a graph G is a collection of edge-disjoint subgraphs whose union is G. We prove that every connected graph can be edge-decomposed into a spanning tree, an even graph, and a star forest. The removal of the edges of a spanning tree results in a collection of cycles and paths. Every connected cubic graph can be decomposed into a spanning tree, a collection of cycles, and a matching.
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