A proof of Ringel's conjecture
A typical decomposition question asks whether the edges of some graph G can be
partitioned into disjoint copies of another graph H. One of the oldest and best known …
partitioned into disjoint copies of another graph H. One of the oldest and best known …
Resolution of the Oberwolfach problem
The Oberwolfach problem, posed by Ringel in 1967, asks for a decomposition of K2n+ 1 into
edge-disjoint copies of a given 2-factor. We show that this can be achieved for all large n …
edge-disjoint copies of a given 2-factor. We show that this can be achieved for all large n …
Embedding rainbow trees with applications to graph labelling and decomposition
A subgraph of an edge-coloured graph is called rainbow if all its edges have distinct colours.
The study of rainbow subgraphs goes back more than two hundred years to the work of …
The study of rainbow subgraphs goes back more than two hundred years to the work of …
Optimal packings of bounded degree trees
We prove that if T1,..., Tn is a sequence of bounded degree trees such that Ti has i vertices,
then Kn has a decomposition into T1,..., Tn. This shows that the tree packing conjecture of …
then Kn has a decomposition into T1,..., Tn. This shows that the tree packing conjecture of …
A blow-up lemma for approximate decompositions
We develop a new method for constructing approximate decompositions of dense graphs
into sparse graphs and apply it to long-standing decomposition problems. For instance, our …
into sparse graphs and apply it to long-standing decomposition problems. For instance, our …
Ringel's tree packing conjecture in quasirandom graphs
P Keevash, K Staden - arxiv preprint arxiv:2004.09947, 2020 - arxiv.org
arxiv:2004.09947v1 [math.CO] 21 Apr 2020 Page 1 Ringel’s tree packing conjecture in
quasirandom graphs Peter Keevash∗ Katherine Staden† April 22, 2020 Abstract We prove that …
quasirandom graphs Peter Keevash∗ Katherine Staden† April 22, 2020 Abstract We prove that …
Extremal aspects of graph and hypergraph decomposition problems.
Extremal aspects of graph and hypergraph decomposition problems. Page 245 Extremal aspects
of graph and hypergraph decomposition problems Stefan Glock Daniela Kühn Deryk Osthus …
of graph and hypergraph decomposition problems Stefan Glock Daniela Kühn Deryk Osthus …
[HTML][HTML] Packing degenerate graphs
Given D and γ> 0, whenever c> 0 is sufficiently small and n sufficiently large, if G is a family
of D-degenerate graphs of individual orders at most n, maximum degrees at most cn log n …
of D-degenerate graphs of individual orders at most n, maximum degrees at most cn log n …
The generalised Oberwolfach problem
P Keevash, K Staden - Journal of Combinatorial Theory, Series B, 2022 - Elsevier
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Packing trees of unbounded degrees in random graphs
In this paper, we address the problem of packing large trees in G n, p. In particular, we prove
the following result. Suppose that T 1,…, TN are n‐vertex trees, each of which has maximum …
the following result. Suppose that T 1,…, TN are n‐vertex trees, each of which has maximum …