ANTI-RAMSEY NUMBER OF EDGE-DISJOINT RAINBOW SPANNING TREES.

An edge-colored graph G is called rainbow if every edge of G receives a different color. The anti-Ramsey number of t edge-disjoint rainbow spanning trees, denoted by r(n,t), is defined as the maximum number of colors in an edge-coloring of Kn containing no t edge-disjoint rainbow spanning trees. Jahanbekam and West [J. Graph Theory, 2014] conjectured that for any fixed t, r(n,t)=(n-22)+t whenever n≥2t+2≥6. In this paper, we prove this conjecture. We also determine r(n,t) when n=2t+1. Together with previous results, this gives the anti-Ramsey number of t edge-disjoint rainbow spanning trees for all values of n and t. [ABSTRACT FROM AUTHOR]