TY - JOUR

T1 - Gap-planar graphs

AU - Bae, Sang Won

AU - Baffier, Jean Francois

AU - Chun, Jinhee

AU - Eades, Peter

AU - Eickmeyer, Kord

AU - Grilli, Luca

AU - Hong, Seok Hee

AU - Korman, Matias

AU - Montecchiani, Fabrizio

AU - Rutter, Ignaz

AU - Tóth, Csaba D.

N1 - Funding Information:
Partially supported by the NSF awards CCF-1422311 and CCF-1423615.
Publisher Copyright:
© 2018 Elsevier B.V.

PY - 2018/10/12

Y1 - 2018/10/12

N2 - We introduce the family of k-gap-planar graphs 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 k of its crossings. This definition is motivated by applications in edge casing, as a k-gap-planar graph can be drawn crossing-free after introducing at most k local gaps per edge. We present results on the maximum density of k-gap-planar graphs, their relationship to other classes of beyond-planar graphs, characterization of k-gap-planar complete graphs, and the computational complexity of recognizing k-gap-planar graphs.

AB - We introduce the family of k-gap-planar graphs 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 k of its crossings. This definition is motivated by applications in edge casing, as a k-gap-planar graph can be drawn crossing-free after introducing at most k local gaps per edge. We present results on the maximum density of k-gap-planar graphs, their relationship to other classes of beyond-planar graphs, characterization of k-gap-planar complete graphs, and the computational complexity of recognizing k-gap-planar graphs.

KW - Beyond planarity k-gap-planar graphs

KW - Complete graphs

KW - Density results

KW - Recognition problem

KW - k-planar graphs

KW - k-quasiplanar graphs

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U2 - 10.1016/j.tcs.2018.05.029

DO - 10.1016/j.tcs.2018.05.029

M3 - Article

AN - SCOPUS:85048165888

SN - 0304-3975

VL - 745

SP - 36

EP - 52

JO - Theoretical Computer Science

JF - Theoretical Computer Science

ER -