Triangle Detection Conjecture

Let $G$ be an input graph with $n$ vertices and $m$ edges. An algorithm runs in the word RAM model with word size $O(\log n)$ bits. Triangle Detection Conjecture. There exists $\gamma > 0$ such that any algorithm to decide whether $G$ is triangle-free requires $\Omega(m^{1+\gamma})$ time in expectation. This is a standard fine-grained hardness assumption for triangle detection and is used as the foundation for complexity-theoretic lower bounds on subgraph counting in bounded-degeneracy graphs.