B1-EPG representations using block-cutpoint trees

In this paper, we are interested in the edge intersection graphs of paths of a grid where each path has at most one bend, called B1-EPG graphs and first introduced by Golumbic et al (2009). We also consider a proper subclass of B1-EPG, the L-EPG graphs, which allows paths only in ``L'' shape. We show that two superclasses of trees are B1-EPG (one of them being the cactus graphs). On the other hand, we show that the block graphs are L-EPG and provide a linear time algorithm to produce L-EPG representations of generalization of trees. These proofs employed a new technique from previous results in the area based on block-cutpoint trees of the respective graphs.