English

B1-EPG representations using block-cutpoint trees

Combinatorics 2021-06-11 v1 Discrete Mathematics

Abstract

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.

Keywords

Cite

@article{arxiv.2106.05312,
  title  = {B1-EPG representations using block-cutpoint trees},
  author = {V. T. F. Luca and F. S. Oliveira and J. L. Szwarcfiter},
  journal= {arXiv preprint arXiv:2106.05312},
  year   = {2021}
}

Comments

9 pages, 13 figures

R2 v1 2026-06-24T03:01:40.809Z