4 papers · 2 filters
An Erdős-Pósa theorem for cycles and faces of distinct lengths
J. Pascal Gollin, Maximilian Gorsky, Meike Hatzel +6
We show that for every , every graph contains vertex-disjoint cycles of different lengths, or there exists a set with $|X| \in \mathcal…
The structure of group-labeled graphs forbidding an immersion
Rose McCarty, Caleb McFarland, Paul Wollan
A -labeled graph is an oriented graph with edges invertibly labeled by a group . We prove a structure theorem for -labeled graphs which forbid a fixed -labeled graph as…
Graphs whose Eulerian trails have unique labels
Donggyu Kim, Rose McCarty, Caleb McFarland
Consider an undirected graph whose edges are labeled invertibly in a group. When does every Eulerian trail from one fixed vertex to another have the same label? We give a precise s…
Totally -Modular Tree Decompositions of Graphic Matrices for Integer Programming
Caleb McFarland
We introduce the tree-decomposition-based parameter totally -modular treewidth (TDM-treewidth) for matrices with two nonzero entries per row. We show how to solve integer progra…