Gap-planar graphs

Sang Won Bae; Jean Francois Baffier; Jinhee Chun; Peter Eades; Kord Eickmeyer; Luca Grilli; Seok Hee Hong; Matias Korman; Fabrizio Montecchiani; Ignaz Rutter; Csaba D. Tóth

doi:10.1007/978-3-319-73915-1_41

Gap-planar graphs

Sang Won Bae, Jean Francois Baffier, Jinhee Chun, Peter Eades, Kord Eickmeyer, Luca Grilli, Seok Hee Hong, Matias Korman, Fabrizio Montecchiani, Ignaz Rutter, Csaba D. Tóth

INF - System Information Sciences

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

3 Citations (Scopus)

Abstract

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 finds motivation in edge casing, as a k-gap-planar graph can be drawn crossing-free after introducing at most k local gaps per edge. We obtain results on the maximum density, drawability of complete graphs, complexity of the recognition problem, and relationships with other families of beyond-planar graphs.

Original language	English
Title of host publication	Graph Drawing and Network Visualization - 25th International Symposium, GD 2017, Revised Selected Papers
Editors	Kwan-Liu Ma, Fabrizio Frati
Publisher	Springer Verlag
Pages	531-545
Number of pages	15
ISBN (Print)	9783319739144
DOIs	https://doi.org/10.1007/978-3-319-73915-1_41
Publication status	Published - 2018
Event	25th International Symposium on Graph Drawing and Network Visualization, GD 2017 - Boston, United States Duration: 2017 Sep 25 → 2017 Sep 27

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	10692 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Other

Other	25th International Symposium on Graph Drawing and Network Visualization, GD 2017
Country	United States
City	Boston
Period	17/9/25 → 17/9/27

ASJC Scopus subject areas

Theoretical Computer Science
Computer Science(all)

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10.1007/978-3-319-73915-1_41

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Bae, S. W., Baffier, J. F., Chun, J., Eades, P., Eickmeyer, K., Grilli, L., Hong, S. H., Korman, M., Montecchiani, F., Rutter, I., & Tóth, C. D. (2018). Gap-planar graphs. In K-L. Ma, & F. Frati (Eds.), Graph Drawing and Network Visualization - 25th International Symposium, GD 2017, Revised Selected Papers (pp. 531-545). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 10692 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-319-73915-1_41

Gap-planar graphs. / Bae, Sang Won; Baffier, Jean Francois; Chun, Jinhee; Eades, Peter; Eickmeyer, Kord; Grilli, Luca; Hong, Seok Hee; Korman, Matias; Montecchiani, Fabrizio; Rutter, Ignaz; Tóth, Csaba D.

Graph Drawing and Network Visualization - 25th International Symposium, GD 2017, Revised Selected Papers. ed. / Kwan-Liu Ma; Fabrizio Frati. Springer Verlag, 2018. p. 531-545 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 10692 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Bae, SW, Baffier, JF, Chun, J, Eades, P, Eickmeyer, K, Grilli, L, Hong, SH, Korman, M, Montecchiani, F, Rutter, I & Tóth, CD 2018, Gap-planar graphs. in K-L Ma & F Frati (eds), Graph Drawing and Network Visualization - 25th International Symposium, GD 2017, Revised Selected Papers. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 10692 LNCS, Springer Verlag, pp. 531-545, 25th International Symposium on Graph Drawing and Network Visualization, GD 2017, Boston, United States, 17/9/25. https://doi.org/10.1007/978-3-319-73915-1_41

Bae SW, Baffier JF, Chun J, Eades P, Eickmeyer K, Grilli L et al. Gap-planar graphs. In Ma K-L, Frati F, editors, Graph Drawing and Network Visualization - 25th International Symposium, GD 2017, Revised Selected Papers. Springer Verlag. 2018. p. 531-545. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-319-73915-1_41

Bae, Sang Won ; Baffier, Jean Francois ; Chun, Jinhee ; Eades, Peter ; Eickmeyer, Kord ; Grilli, Luca ; Hong, Seok Hee ; Korman, Matias ; Montecchiani, Fabrizio ; Rutter, Ignaz ; Tóth, Csaba D. / Gap-planar graphs. Graph Drawing and Network Visualization - 25th International Symposium, GD 2017, Revised Selected Papers. editor / Kwan-Liu Ma ; Fabrizio Frati. Springer Verlag, 2018. pp. 531-545 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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abstract = "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 finds motivation in edge casing, as a k-gap-planar graph can be drawn crossing-free after introducing at most k local gaps per edge. We obtain results on the maximum density, drawability of complete graphs, complexity of the recognition problem, and relationships with other families of beyond-planar graphs.",

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note = "Funding Information: Research started at the NII Shonan Meeting “Algorithmics for Beyond Planar Graphs.” The authors thank the organizers, and Yota Otachi for useful discussions. Bae was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2015R1D1A1A01057220). Baffier was supported by JST-ERATO Grant Number JPMJER1201, Japan. Eades and Hong were partially supported by ARC DP160104148. Korman was partially supported by MEXT KAKENHI No. 15H02665, 17K12635 and JST ERATO Grant Number JPMJER1305. T{\'o}th was supported in part by the NSF awards CCF-1422311 and CCF-1423615.; 25th International Symposium on Graph Drawing and Network Visualization, GD 2017 ; Conference date: 25-09-2017 Through 27-09-2017",

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doi = "10.1007/978-3-319-73915-1_41",

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AU - Hong, Seok Hee

AU - Korman, Matias

AU - Montecchiani, Fabrizio

AU - Rutter, Ignaz

AU - Tóth, Csaba D.

N1 - Funding Information: Research started at the NII Shonan Meeting “Algorithmics for Beyond Planar Graphs.” The authors thank the organizers, and Yota Otachi for useful discussions. Bae was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2015R1D1A1A01057220). Baffier was supported by JST-ERATO Grant Number JPMJER1201, Japan. Eades and Hong were partially supported by ARC DP160104148. Korman was partially supported by MEXT KAKENHI No. 15H02665, 17K12635 and JST ERATO Grant Number JPMJER1305. Tóth was supported in part by the NSF awards CCF-1422311 and CCF-1423615.

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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 finds motivation in edge casing, as a k-gap-planar graph can be drawn crossing-free after introducing at most k local gaps per edge. We obtain results on the maximum density, drawability of complete graphs, complexity of the recognition problem, and relationships with other families of beyond-planar graphs.

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Gap-planar graphs

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