TY - GEN

T1 - Turning cliques into paths to achieve planarity

AU - Angelini, Patrizio

AU - Eades, Peter

AU - Hong, Seok Hee

AU - Klein, Karsten

AU - Kobourov, Stephen

AU - Liotta, Giuseppe

AU - Navarra, Alfredo

AU - Tappini, Alessandra

N1 - Funding Information:
This work began at the Bertinoro Workshop on Graph Drawing 2018. Research was partially supported by DFG grant Ka812/17-1 and MIUR-DAAD Joint Mobility Program n.57397196 (PA), by Young Scholar Fund/AFF-Univ. Konstanz (KK), by NSF grants CCF-1740858-CCF-1712119 (SK), by project “Algoritmi e sistemi di analisi visuale di reti complesse e di grandi dimensioni”-Ric. di Base 2018, Dip. Ingegneria-Univ. Perugia (GL, AT), by project GEO-SAFE n.H2020-691161 (AN).
Funding Information:
This work began at the Bertinoro Workshop on Graph Drawing 2018. Research was partially supported by DFG grant Ka812/17-1 and MIUR-DAAD Joint Mobility Program n.57397196 (PA), by Young Scholar Fund/AFF - Univ. Konstanz (KK), by NSF grants CCF-1740858 - CCF-1712119 (SK), by project “Algoritmi e sistemi di analisi visuale di reti complesse e di grandi dimensioni” - Ric. di Base 2018, Dip. Ingegneria - Univ. Perugia (GL, AT), by project GEO-SAFE n.H2020-691161 (AN).

PY - 2018

Y1 - 2018

N2 - Motivated by hybrid graph representations, we introduce and study the following beyond-planarity problem, which we call h-Clique2Path Planarity: Given a graph G, whose vertices are partitioned into subsets of size at most h, each inducing a clique, remove edges from each clique so that the subgraph induced by each subset is a path, in such a way that the resulting subgraph of G is planar. We study this problem when G is a simple topological graph, and establish its complexity in relation to k-planarity. We prove that h-Clique2Path Planarity is NP-complete even when h=4 and G is a simple 3-plane graph, while it can be solved in linear time, for any h, when G is 1-plane.

AB - Motivated by hybrid graph representations, we introduce and study the following beyond-planarity problem, which we call h-Clique2Path Planarity: Given a graph G, whose vertices are partitioned into subsets of size at most h, each inducing a clique, remove edges from each clique so that the subgraph induced by each subset is a path, in such a way that the resulting subgraph of G is planar. We study this problem when G is a simple topological graph, and establish its complexity in relation to k-planarity. We prove that h-Clique2Path Planarity is NP-complete even when h=4 and G is a simple 3-plane graph, while it can be solved in linear time, for any h, when G is 1-plane.

UR - http://www.scopus.com/inward/record.url?scp=85059092003&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85059092003&partnerID=8YFLogxK

U2 - 10.1007/978-3-030-04414-5_5

DO - 10.1007/978-3-030-04414-5_5

M3 - Conference contribution

AN - SCOPUS:85059092003

SN - 9783030044138

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 67

EP - 74

BT - Graph Drawing and Network Visualization - 26th International Symposium, GD 2018, Proceedings

A2 - Biedl, Therese

A2 - Kerren, Andreas

PB - Springer-Verlag

T2 - 26th International Symposium on Graph Drawing and Network Visualization, GD 2018

Y2 - 26 September 2018 through 28 September 2018

ER -