Twin-Width Meets Feedback Edges and Vertex Integrity

J Balabán, R Ganian, M Rocton - arxiv preprint arxiv:2407.15514, 2024 - arxiv.org
The approximate computation of twin-width has attracted significant attention already since
the moment the parameter was introduced. A recently proposed approach (STACS 2024) …

Linear Layouts of Bipartite Planar Graphs

H Förster, M Kaufmann, L Merker, S Pupyrev… - Algorithms and Data …, 2023 - Springer
A linear layout of a graph G consists of a linear order,≺, of the vertices and a partition of the
edges. A part is called a queue (stack) if no two edges nest (cross), that is, two edges (v, w) …

Weakly Leveled Planarity with Bounded Span

M Bekos, G Da Lozzo, F Frati, S Gupta… - arxiv preprint arxiv …, 2024 - arxiv.org
This paper studies planar drawings of graphs in which each vertex is represented as a point
along a sequence of horizontal lines, called levels, and each edge is either a horizontal …

Fixed-Parameter Algorithms for Computing RAC Drawings of Graphs

C Brand, R Ganian, S Röder, F Schager - International Symposium on …, 2023 - Springer
In a right-angle crossing (RAC) drawing of a graph, each edge is represented as a polyline
and edge crossings must occur at an angle of exactly 90∘, where the number of bends on …

Vertex-bipartition: A unified approach for kernelization of graph linear layout problems parameterized by vertex cover

Y Liu, Y Li, J Huang - … Journal of Foundations of Computer Science, 2024 - World Scientific
The Linear Layout of Graphs problem asks, given a graph G and a positive integer k,
whether G admits a layout consisting of a linear ordering of its vertices and a partition of its …

Pathways to Tractability for Geometric Thickness

T Depian, SD Fink, A Firbas, R Ganian… - … Conference on Current …, 2025 - Springer
We study the classical problem of computing geometric thickness, ie, finding a straight-line
drawing of an input graph and a partition of its edges into as few parts as possible so that …

The parametrized complexity of the segment number

S Cornelsen, G Da Lozzo, L Grilli, S Gupta… - … Symposium on Graph …, 2023 - Springer
Given a straight-line drawing of a graph, a segment is a maximal set of edges that form a line
segment. Given a planar graph G, the segment number of G is the minimum number of …

Fixed-Parameter Algorithms for Computing Bend-Restricted RAC Drawings of Graphs

C Brand, R Ganian, S Röder, F Schager - Journal of Graph Algorithms and …, 2024 - jgaa.info
In a right-angle crossing (RAC) drawing of a graph, each edge is represented as a polyline
and edge crossings must occur at an angle of exactly $90^\circ $, where the number of …

Parameterized Algorithms for Fixed-Order Book Drawing with Few Crossings Per Edge

J Huang, J Chen, Y Liu, G **ao… - International Journal of …, 2024 - World Scientific
Given an n-vertex graph G with a fixed linear ordering of V (G) and two integers k, b, the
problem fixed-order book drawing with few crossings per edge asks whether or not G admits …

A Faster Parameterized Algorithm for Bipartite 1-Sided Vertex Explosion

Y Liu, G **ao, A Liu, D Wu, J Huang - International Conference on …, 2023 - Springer
Given a bipartite graph G=(T∪ B, E), the problem bipartite 1-sided vertex explosion is to
decide whether there exists a planar 2-layer embedding of G after exploding at most k …