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View article: Tight Bounds for Some Classical Problems Parameterized by Cutwidth
Tight Bounds for Some Classical Problems Parameterized by Cutwidth Open
Cutwidth is a widely studied parameter and it quantifies how well a graph can be decomposed along small edge-cuts. It complements pathwidth, which captures decomposition by small vertex separators, and it is well-known that cutwidth upper-…
View article: Half-integral Erdős-Pósa property for non-null $S$-$T$ paths
Half-integral Erdős-Pósa property for non-null $S$-$T$ paths Open
For a group $Γ$, a $Γ$-labelled graph is an undirected graph $G$ where every orientation of an edge is assigned an element of $Γ$ so that opposite orientations of the same edge are assigned inverse elements. A path in $G$ is non-null if th…
View article: Space-Efficient Parameterized Algorithms on Graphs of Low Shrubdepth
Space-Efficient Parameterized Algorithms on Graphs of Low Shrubdepth Open
Dynamic programming on various graph decompositions is one of the most fundamental techniques used in parameterized complexity. Unfortunately, even if we consider concepts as simple as path or tree decompositions, such dynamic programming …
View article: Tight Bounds for Connectivity Problems Parameterized by Cutwidth
Tight Bounds for Connectivity Problems Parameterized by Cutwidth Open
In this work we start the investigation of tight complexity bounds for connectivity problems parameterized by cutwidth assuming the Strong Exponential-Time Hypothesis (SETH). Van Geffen et al. [Bas A. M. van Geffen et al., 2020] posed this…
View article: Space-Efficient Parameterized Algorithms on Graphs of Low Shrubdepth
Space-Efficient Parameterized Algorithms on Graphs of Low Shrubdepth Open
Dynamic programming on various graph decompositions is one of the most fundamental techniques used in parameterized complexity. Unfortunately, even if we consider concepts as simple as path or tree decompositions, such dynamic programming …
View article: Tight Algorithmic Applications of Clique-Width Generalizations
Tight Algorithmic Applications of Clique-Width Generalizations Open
In this work, we study two natural generalizations of clique-width introduced by Martin Fürer. Multi-clique-width (mcw) allows every vertex to hold multiple labels [ITCS 2017], while for fusion-width (fw) we have a possibility to merge all…
View article: Polychromatic Colorings of Unions of Geometric Hypergraphs
Polychromatic Colorings of Unions of Geometric Hypergraphs Open
We consider the polychromatic coloring problems for unions of two or more geometric hypergraphs on the same vertex sets of points in the plane. We show, inter alia, that the union of bottomless rectangles and horizontal strips does in gene…
View article: Drawing Two Posets
Drawing Two Posets Open
We investigate the problem of drawing two posets of the same ground set so that one is drawn from left to right and the other one is drawn from the bottom up. The input to this problem is a directed graph $G = (V, E)$ and two sets $X, Y$ w…
View article: Drawing Two Posets
Drawing Two Posets Open
We investigate the problem of drawing two posets of the same ground set so that one is drawn from left to right and the other one is drawn from the bottom up. The input to this problem is a directed graph $G = (V, E)$ and two sets $X, Y$ w…