  Augustine et al. [DISC 2022] initiated the study of distributed graph
algorithms in the presence of Byzantine nodes in the congested clique model. In
this model, there is a set $B$ of Byzantine nodes, where $|B|$ is less than a
third of the total number of nodes. These nodes have complete knowledge of the
network and the state of other nodes, and they conspire to alter the output of
the system. The authors addressed the connectivity problem, showing that it is
solvable under the promise that either the subgraph induced by the honest nodes
is connected, or the graph has $2|B|+1$ connected components.
  In the current work, we continue the study of the Byzantine congested clique
model by considering the recognition of other graph properties, specifically
\emph{hereditary properties}. A graph property is \emph{hereditary} if it is
closed under taking induced subgraphs. Examples of hereditary properties
include acyclicity, bipartiteness, planarity, and bounded (chromatic,
independence) number, etc.
  For each class of graphs $\mathcal{G}$ satisfying an hereditary property (an
hereditary graph-class), we propose a randomized algorithm which, with high
probability, (1) accepts if the input graph $G$ belongs to $\mathcal{G}$, and
(2) rejects if $G$ contains at least $|B| + 1$ disjoint subgraphs not belonging
to $\mathcal{G}$. The round complexity of our algorithm is
$$\mathcal{O}\left(\left(\dfrac{\log
\left(\left|\mathcal{G}_n\right|\right)}{n}
+|B|\right)\cdot\textrm{polylog}(n)\right),$$ where $\mathcal{G}_n$ is the set
of $n$-node graphs in $\mathcal{G}$.
  Finally, we obtain an impossibility result that proves that our result is
tight. Indeed, we consider the hereditary class of acyclic graphs, and we prove
that there is no algorithm that can distinguish between a graph being acyclic
and a graph having $|B|$ disjoint cycles.
