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math.CO2026
Biclique decompositions from Welzl orders
Jean Cardinal, Rose McCarty, Yelena Yuditsky
A biclique decomposition of a graph is a partition of its edges into complete bipartite subgraphs. We consider graphs whose vertices can be ordered such that the neighborhood of ev…
math.CO2026
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…
math.CO2026
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…