 to the best of our knowledge, the state-of-the-art distributed algorithm for this problem with a message complexity of o  (m^{3/4}) incurs a round complexity of \Omega(m^{1/3 (m^{2/3) and an amortized round complexityof }%DIFDELCMD < \tilde{O}(1) %%% under fully dynamic edge updates in the CONGEST model, where%DIFDELCMD < \tilde{O}%%% (\cdot) suppresses polylogarithmic factors. 
<clarity>  to the best of our knowledge, the state-of-the-art distributed algorithm for this problem with a message complexity of o  (m^{3/4}) incurs a round complexity of \Omega(m^{1/3 (m^{2/3) and an amortized round complexityof }%DIFDELCMD < \tilde{O}(1) %%% under fully dynamic edge updates in the CONGEST model, where%DIFDELCMD < \tilde{O}%%% (\cdot) suppresses polylogarithmic factors. 
 to the best of our knowledge, the state-of-the-art distributed algorithm for this problem with a message complexity of o (m^{3/4}) (m^{2/3) and an amortized round complexityof }%DIFDELCMD < \tilde{O}(1) %%% under fully dynamic edge updates in the CONGEST model, where%DIFDELCMD < \tilde{O}%%% (\cdot) suppresses polylogarithmic factors. 