A survey that maps the results and methods for finding rainbow subgraphs in edge-colored graphs, and their applications across discrete mathematics, coding theory, and computer science.
Ringel's tree packing conjecture in quasirandom graphs
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abstract
We prove that any quasirandom graph with $n$ vertices and $rn$ edges can be decomposed into $n$ copies of any fixed tree with $r$ edges. The case of decomposing a complete graph establishes a conjecture of Ringel from 1963.
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Restricted subgraphs of edge-colored graphs and applications
A survey that maps the results and methods for finding rainbow subgraphs in edge-colored graphs, and their applications across discrete mathematics, coding theory, and computer science.