4 papers
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…
Almost all graphs are vertex-minor universal
Ruben Ascoli, Bryce Frederickson, Sarah Frederickson +2
Answering a question of Claudet, we prove that the uniformly random graph is -vertex-minor universal with high probability. That is, for some…
Odd-Cycle-Packing-treewidth: On the Maximum Independent Set problem in odd-minor-free graph classes
Mujin Choi, Maximilian Gorsky, Gunwoo Kim +2
We introduce the tree-decomposition-based graph parameter Odd-Cycle-Packing-treewidth (OCP-tw) as a width parameter that asks to decompose a given graph into pieces of bounded odd…