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            <title xml:lang="fr">Some properties of edge intersection graphs of single-bend paths on a grid</title>
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                <term xml:lang="fr">Erdős–Hajnal property</term>
                <term xml:lang="fr">Neighborhood</term>
                <term xml:lang="fr">Chordal graphs</term>
                <term xml:lang="fr">Paths on a grid</term>
                <term xml:lang="fr">Intersection graphs</term>
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              <p>In this paper we consider graphs G whose vertices can be represented as single-bend paths (i.e., paths with at most one turn) on a rectangular grid, such that two vertices are adjacent in G if and only if the corresponding paths share at least one edge of the grid. These graphs, called B1-EPG graphs, were first introduced in Golumbic et al. (2009) [13]. Here we show that the neighborhood of every vertex in a B1-EPG graph induces a weakly chordal graph. From this we conclude that the family F of B1-EPG graphs satisfies the Erdős–Hajnal property with View the MathML source, i.e., that every B1-EPG graph on n vertices contains either a clique or a stable set of size at least View the MathML source. Finally we give a characterization of B1-EPG graphs among some subclasses of chordal graphs, namely chordal bull-free graphs, chordal claw-free graphs, chordal diamond-free graphs, and special cases of split graphs.</p>
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