  In this paper, we revisit the problem of classical \textit{meeting times} of
random walks in graphs. In the process that two tokens (called agents) perform
random walks on an undirected graph, the meeting times are defined as the
expected times until they meet when the two agents are initially located at
different vertices. A key feature of the problem is that, in each discrete
time-clock (called \textit{round}) of the process, the scheduler selects only
one of the two agents, and the agent performs one move of the random walk. In
the adversarial setting, the scheduler utilizes the strategy that intends to
\textit{maximizing} the expected time to meet.
  In the seminal papers \cite{collisions,israeli1990token,tetali1993simult},
for the random walks of two agents, the notion of \textit{atomicity} is
implicitly considered. That is, each move of agents should complete while the
other agent waits. In this paper, we consider and formalize the meeting time of
\textit{non-atomic} random walks. In the non-atomic random walks, we assume
that in each round, only one agent can move but the move does not necessarily
complete in the next round. In other words, we assume that an agent can move at
a round while the other agent is still moving on an edge. For the non-atomic
random walks with the adversarial schedulers, we give a polynomial upper bound
on the meeting times.
