B1-EPG representations using block-cutpoint trees

Vitor Tocci Ferreira de Luca, Fabiano de Souza Oliveira, Jayme Luiz Szwarcfiter


In this paper, we are interested in the edge intersection graphs of paths of a grid whereeach 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, thex-EPG graphs, which allows paths onlyin “x” shape. We show that two superclasses of trees are B1-EPG (one of them being the cactusgraphs). On the other hand, we show that the block graphs arex-EPG and provide a linear timealgorithm to producex-EPG representations of generalization of trees. These proofs employed anew technique from previous results in the area based on block-cutpoint trees of the respectivegraphs.


Edge intersection graph; Block-cutpoint trees; Block graphs; Cactus graphs

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DOI: https://doi.org/10.5540/03.2021.008.01.0379


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