The Path Partition Conjecture is True and its Validity Yields Upper Bounds for Detour Chromatic Number and Star Chromatic Number

G. Sethuraman

The detour order of a graph $G$, denoted $\tau (G)$, is the order of a longest path in $G$. A partition $(A,B)$ of $V(G)$ such that $\tau (⟨A⟩)\le a$ and $τ(\langle B \ran…