Jahanbekam–West anti-Ramsey conjecture for edge-disjoint rainbow spanning trees

Jahanbekam and West proposed the conjecture in 2016. It predicts the exact largest number of colors possible without $t$ edge-disjoint rainbow spanning trees when $n\geq 2t+2\geq 6$.

Known results

• The case $t=1$ was established by Bialostocki and Voxman.
• The case $t=2$ was established by Akbari and Alipour.
• Jahanbekam and West supplied the lower-bound constructions.

February 24, 2018 claimed resolution

Lu and Wang’s paper Anti-Ramsey number of edge-disjoint rainbow spanning trees states that it proves

$$r(n,t)=\binom{n-2}{2}+t$$

for $n\geq 2t+2\geq 6$, matching the conjecture. It also claims to determine the boundary cases $n=2t+1$ and $n=2t$, so the full problem is settled according to the paper; this resolution is unverified in this summary.

Current status (as of September 2026): The conjecture is claimed proved, with no unresolved cases reported in its stated range, but this automated summary does not independently verify the proof.