  Beame et al. [ITCS 2018 & TALG 2021] introduced and used the Bipartite
Independent Set (BIS) and Independent Set (IS) oracle access to an unknown,
simple, unweighted and undirected graph and solved the edge estimation problem.
The introduction of this oracle set forth a series of works in a short span of
time that either solved open questions mentioned by Beame et al. or were
generalizations of their work as in Dell and Lapinskas [STOC 2018], Dell,
Lapinskas and Meeks [SODA 2020], Bhattacharya et al. [ISAAC 2019 & Theory
Comput. Syst. 2021], and Chen et al. [SODA 2020]. Edge estimation using BIS can
be done using polylogarithmic queries, while IS queries need sub-linear but
more than polylogarithmic queries. Chen et al. improved Beame et al.'s upper
bound result for edge estimation using IS and also showed an almost matching
lower bound. Beame et al. in their introductory work asked a few open questions
out of which one was on estimating structures of higher order than edges, like
triangles and cliques, using BIS queries.
  In this work, we completely resolve the query complexity of estimating
triangles using BIS oracle. While doing so, we prove a lower bound for an even
stronger query oracle called Edge Emptiness (EE) oracle, recently introduced by
Assadi, Chakrabarty and Khanna [ESA 2021] to test graph connectivity.
