33 papers
Dynamic domination and independence in sparse graphs
BartÅomiej Bosek, Wojciech Nadara, MichaÅ Pilipczuk +1
Let be a class of graphs of bounded expansion and be fixed. We give a dynamic data structure that for a given dynamic graph , updated by edge i…
Fatness and Flatness
Arnold Filtser, Hung Le, Nikolas Mählmann +2
Fat minors are the metric analog of graph minors that are tailored to the analysis of metric (edge-weighted) graphs and, more generally, metric spaces having a suitable notion of s…
Neighborhood Complexity and Radius-1 Merge-Width in Monadically Dependent Graph Classes
Jan Dreier, Nikolas Mählmann, Rose McCarty +2
Monadic dependence is a proposed structural dividing line for fixed-parameter tractability of first-order model checking on hereditary graph classes. A graph class is \emph{monadic…
A coarse block-cut tree theorem
Júlia Baligács, Václav Blažej, Jadwiga Czyżewska +2
We prove a coarse analogue of the classic fact that every graph can be decomposed along its cut-vertices into -connected components. Precisely, we prove that for every graph …
A coarse Menger's Theorem for planar and bounded genus graphs
Václav Blažej, MichaŠPilipczuk, Evangelos Protopapas
Menger's Theorem is a fundamental result in graph theory. It states that if in a graph with distinguished sets of terminal vertices and there are no pairwise vertex…
Dynamic Detours
Daniel Dadush, MichaÅ Pilipczuk, Amadeus Reinald +2
Fix a parameter . We give dynamic data structures that for a fully dynamic undirected graph , updated over time by edge insertions and edge deletions, can answe…