Two conjectures on vertex-disjoint rainbow triangles

Xu Liu, Bo Ning, Yuting Tian

In 1963, Dirac proved that every $n$-vertex graph has $k$ vertex-disjoint triangles if $n\ge 3k$ and minimum degree $\delta (G)\ge \frac{n+k}{2}$. The base case $n=3k$ can be reduced t…