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 conjectures in this area, posed by Ringel in 1963, concerns the decomposition of complete graphs into edge-disjoint copies of a tree....
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| Published in | Geometric and functional analysis Vol. 31; no. 3; pp. 663 - 720 |
|---|---|
| Main Authors | , , |
| Format | Journal Article |
| Language | English |
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Cham
Springer International Publishing
01.06.2021
Springer Nature B.V |
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| Abstract | 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 conjectures in this area, posed by Ringel in 1963, concerns the decomposition of complete graphs into edge-disjoint copies of a tree. It says that any tree with
n
edges packs
2
n
+
1
times into the complete graph
K
2
n
+
1
. In this paper, we prove this conjecture for large
n
. |
|---|---|
| AbstractList | 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 conjectures in this area, posed by Ringel in 1963, concerns the decomposition of complete graphs into edge-disjoint copies of a tree. It says that any tree with n edges packs 2n+1 times into the complete graph K2n+1. In this paper, we prove this conjecture for large n. 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 conjectures in this area, posed by Ringel in 1963, concerns the decomposition of complete graphs into edge-disjoint copies of a tree. It says that any tree with n edges packs $$2n+1$$ 2 n + 1 times into the complete graph $$K_{2n+1}$$ K 2 n + 1 . In this paper, we prove this conjecture for large n . 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 conjectures in this area, posed by Ringel in 1963, concerns the decomposition of complete graphs into edge-disjoint copies of a tree. It says that any tree with n edges packs 2 n + 1 times into the complete graph K 2 n + 1 . In this paper, we prove this conjecture for large n . |
| Author | Montgomery, R. Pokrovskiy, A. Sudakov, B. |
| Author_xml | – sequence: 1 givenname: R. surname: Montgomery fullname: Montgomery, R. organization: School of Mathematics, University of Birmingham – sequence: 2 givenname: A. surname: Pokrovskiy fullname: Pokrovskiy, A. organization: Department of Mathematics, University College London – sequence: 3 givenname: B. surname: Sudakov fullname: Sudakov, B. email: benjamin.sudakov@math.ethz.ch organization: Department of Mathematics, ETH |
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| Snippet | 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... 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... |
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| Title | A proof of Ringel’s conjecture |
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