Paper
Grounded String Representations of Series-Parallel Graphs without Transitive Edges
Authors
Sabine Cornelsen, Jan Kratochvíl, Miriam Münch, Giacomo Ortali, Alexandra Weinberger, Alexander Wolff
Abstract
In a {\em grounded string representation} of a graph there is a horizontal line $\ell$ and each vertex is represented as a simple curve below $\ell$ with one end point on $\ell$ such that two curves intersect if and only if the respective vertices are adjacent. A grounded string representation is a {\em grounded L-reverseL-representation} if each vertex is represented by a 1-bend orthogonal polyline. It is a {\em grounded L-representation} if in addition all curves are L-shaped. We show that every biconnected series-parallel graph without edges between the two vertices of a separation pair (i.e., {\em transitive edges}) admits a grounded L-reverseL-representation if and only if it admits a grounded string representation. Moreover, we can test in linear time whether such a representation exists. We also construct a biconnected series-parallel graph without transitive edges that admits a grounded L-reverseL-representation, but no grounded L-representation.
Metadata
Related papers
Fractal universe and quantum gravity made simple
Fabio Briscese, Gianluca Calcagni • 2026-03-25
POLY-SIM: Polyglot Speaker Identification with Missing Modality Grand Challenge 2026 Evaluation Plan
Marta Moscati, Muhammad Saad Saeed, Marina Zanoni, Mubashir Noman, Rohan Kuma... • 2026-03-25
LensWalk: Agentic Video Understanding by Planning How You See in Videos
Keliang Li, Yansong Li, Hongze Shen, Mengdi Liu, Hong Chang, Shiguang Shan • 2026-03-25
Orientation Reconstruction of Proteins using Coulomb Explosions
Tomas André, Alfredo Bellisario, Nicusor Timneanu, Carl Caleman • 2026-03-25
The role of spatial context and multitask learning in the detection of organic and conventional farming systems based on Sentinel-2 time series
Jan Hemmerling, Marcel Schwieder, Philippe Rufin, Leon-Friedrich Thomas, Mire... • 2026-03-25
Raw Data (Debug)
{
"raw_xml": "<entry>\n <id>http://arxiv.org/abs/2603.02827v1</id>\n <title>Grounded String Representations of Series-Parallel Graphs without Transitive Edges</title>\n <updated>2026-03-03T10:21:39Z</updated>\n <link href='https://arxiv.org/abs/2603.02827v1' rel='alternate' type='text/html'/>\n <link href='https://arxiv.org/pdf/2603.02827v1' rel='related' title='pdf' type='application/pdf'/>\n <summary>In a {\\em grounded string representation} of a graph there is a horizontal line $\\ell$ and each vertex is represented as a simple curve below $\\ell$ with one end point on $\\ell$ such that two curves intersect if and only if the respective vertices are adjacent. A grounded string representation is a {\\em grounded L-reverseL-representation} if each vertex is represented by a 1-bend orthogonal polyline. It is a {\\em grounded L-representation} if in addition all curves are L-shaped. We show that every biconnected series-parallel graph without edges between the two vertices of a separation pair (i.e., {\\em transitive edges}) admits a grounded L-reverseL-representation if and only if it admits a grounded string representation. Moreover, we can test in linear time whether such a representation exists. We also construct a biconnected series-parallel graph without transitive edges that admits a grounded L-reverseL-representation, but no grounded L-representation.</summary>\n <category scheme='http://arxiv.org/schemas/atom' term='cs.CG'/>\n <published>2026-03-03T10:21:39Z</published>\n <arxiv:comment>To appear in Proc. EuroCG 2026</arxiv:comment>\n <arxiv:primary_category term='cs.CG'/>\n <author>\n <name>Sabine Cornelsen</name>\n </author>\n <author>\n <name>Jan Kratochvíl</name>\n </author>\n <author>\n <name>Miriam Münch</name>\n </author>\n <author>\n <name>Giacomo Ortali</name>\n </author>\n <author>\n <name>Alexandra Weinberger</name>\n </author>\n <author>\n <name>Alexander Wolff</name>\n </author>\n </entry>"
}