4 citations · 13 across the 11 of their papers we have counts for
9 papers · 1 filter
Connected (Dense) Partition for Tree-Like Graphs
Katrin Casel, Archontia C. Giannopoulou, Aikaterini Niklanovits
We focus on two variants of graph partitioning problems, connected partition and dense partition. Formally, given a graph and a partition of its vertices $\mathcal P=\{P_…
Combining Crown Structures for Vulnerability Measures
Katrin Casel, Tobias Friedrich, Aikaterini Niklanovits +2
Over the past decades, various metrics have emerged in graph theory to grasp the complex nature of network vulnerability. In this paper, we study two specific measures: (weighted)…
Efficient Constructions for the Győri-Lovász Theorem on Almost Chordal Graphs
Katrin Casel, Tobias Friedrich, Davis Issac +2
In the 1970s, Győri and Lovász showed that for a -connected -vertex graph, a given set of terminal vertices and natural numbers satisfying…
Fixed-Parameter Sensitivity Oracles
Davide Bilò, Katrin Casel, Keerti Choudhary +5
We combine ideas from distance sensitivity oracles (DSOs) and fixed-parameter tractability (FPT) to design sensitivity oracles for FPT graph problems. An oracle with sensitivity $f…
Balanced Crown Decomposition for Connectivity Constraints
Katrin Casel, Tobias Friedrich, Davis Issac +2
We introduce the balanced crown decomposition that captures the structure imposed on graphs by their connected induced subgraphs of a given size. Such subgraphs are a popular model…
Shortest Distances as Enumeration Problem
Katrin Casel, Tobias Friedrich, Stefan Neubert +1
We investigate the single source shortest distance (SSSD) and all pairs shortest distance (APSD) problems as enumeration problems (on unweighted and integer weighted graphs), meani…
From Symmetry to Asymmetry: Generalizing TSP Approximations by Parametrization
Lukas Behrendt, Katrin Casel, Tobias Friedrich +3
We generalize the tree doubling and Christofides algorithm, the two most common approximations for TSP, to parameterized approximations for ATSP. The parameters we consider for the…
Zeros and approximations of Holant polynomials on the complex plane
Katrin Casel, Philipp Fischbeck, Tobias Friedrich +2
We present fully polynomial approximation schemes for a broad class of Holant problems with complex edge weights, which we call Holant polynomials. We transform these problems into…
Graph and String Parameters: Connections Between Pathwidth, Cutwidth and the Locality Number
Katrin Casel, Joel D. Day, Pamela Fleischmann +3
We investigate the locality number, a recently introduced structural parameter for strings (with applications in pattern matching with variables), and its connection to two importa…