On Split \(B_1\)-EPG Graphs
In this paper, we are interested in edge intersection graphs of paths in a grid, such that each such path has at most one bend. These graphs were introduced in  and they are called \(B_1\)-EPG graphs. In particular, we focus on split graphs and characterise those that are \(B_1\)-EPG. This characterisation allows us to disprove a conjecture of Cameron et al. . The existence of polynomial-time recognition algorithm for this graph class is still unknown. We furthermore investigate inclusion relationships among subclasses of split graphs that are \(B_1\)-EPG.
The first author has been supported by the Scientific and Technological Research Council of Turkey (TÜBİTAK) under 2214-A Doctoral Research Program Grant during his stay in Switzerland. This work was done while the first and second authors visited the University of Fribourg, Switzerland. The support of the institution is gratefully acknowledged.
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