  This paper presents a quantum algorithm for triangle finding over sparse
graphs that improves over the previous best quantum algorithm for this task by
Buhrman et al. [SIAM Journal on Computing, 2005]. Our algorithm is based on the
recent $\tilde O(n^{5/4})$-query algorithm given by Le Gall [FOCS 2014] for
triangle finding over dense graphs (here $n$ denotes the number of vertices in
the graph). We show in particular that triangle finding can be solved with
$O(n^{5/4-\epsilon})$ queries for some constant $\epsilon>0$ whenever the graph
has at most $O(n^{2-c})$ edges for some constant $c>0$.
