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Bae, Sang Won,Baffier, Jean-Francois,Chun, Jinhee,Eades, Peter,Eickmeyer, Kord,Grilli, Luca,Hong, Seok-Hee,Korman, Matias,Montecchiani, Fabrizio,Rutter, Ignaz,Tó,th, Csaba D. Elsevier 2018 Theoretical computer science Vol.745 No.-
<P><B>Abstract</B></P> <P>We introduce the family of <I>k-gap-planar graphs</I> for k ≥ 0 , i.e., graphs that have a drawing in which each crossing is assigned to one of the two involved edges and each edge is assigned at most <I>k</I> of its crossings. This definition is motivated by applications in edge casing, as a <I>k</I>-gap-planar graph can be drawn crossing-free after introducing at most <I>k</I> local gaps per edge. We present results on the maximum density of <I>k</I>-gap-planar graphs, their relationship to other classes of beyond-planar graphs, characterization of <I>k</I>-gap-planar complete graphs, and the computational complexity of recognizing <I>k</I>-gap-planar graphs.</P>