-restricted edge-connectivity in triangle-free graphs

Abstract: Let be a -connected graph. is called -optimal, if its -restricted edge-connectivity equals its minimum -edge degree.  is called super- if every -cut isolates a connected subgraph of order . Firstly, we give a lower bound on the order of -fragments in triangle-free graphs that are not -optimal. Secondly, we present an Ore-type condition for triangle-free graphs to be -optimal. Thirdly, we prove a lower bound on the order of -fragments in triangle-free -connected graphs, and use it to show that triangle-free graphs with high minimum degree are -optimal and super-. [Copyright &y& Elsevier]