Rainbow Trees in Hypercubes
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866918127424503808 |
|---|---|
| author | Crawford, Nicholas Sankar, Maya Schildkraut, Carl Spiro, Sam |
| author_facet | Crawford, Nicholas Sankar, Maya Schildkraut, Carl Spiro, Sam |
| contents | We prove that every proper edge-coloring of the $n$-dimensional hypercube $Q_n$ contains a rainbow copy of every tree $T$ on at most $n$ edges. This result is best possible, as $Q_n$ can be properly edge-colored using only $n$ colors while avoiding rainbow cycles. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_14186 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Rainbow Trees in Hypercubes Crawford, Nicholas Sankar, Maya Schildkraut, Carl Spiro, Sam Combinatorics Discrete Mathematics We prove that every proper edge-coloring of the $n$-dimensional hypercube $Q_n$ contains a rainbow copy of every tree $T$ on at most $n$ edges. This result is best possible, as $Q_n$ can be properly edge-colored using only $n$ colors while avoiding rainbow cycles. |
| title | Rainbow Trees in Hypercubes |
| topic | Combinatorics Discrete Mathematics |
| url | https://arxiv.org/abs/2508.14186 |