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Ringel's tree packing conjecture in quasirandom graphs

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arxiv 2004.09947 v1 pith:DZ5ODJ7T submitted 2020-04-21 math.CO

Peter Keevash , Katherine Staden This is my paper · ORCID
classification math.CO
keywords conjectureedgesgraphquasirandomringeltreecasecomplete
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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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  1. Restricted subgraphs of edge-colored graphs and applications

    math.CO 2024-12 conditional novelty 2.0 of 10

    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.

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