collaborators

8 papers

math.CO2026

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…

math.CO2026

Coloring Graphs With No Totally Odd Clique Immersion

Caleb McFarland

We prove that graphs that do not contain a totally odd immersion of are -colorable. In particular, we show that any graph with no totally odd immersion of $K_…

math.CO2026

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 progr…

math.CO2026

The independence ratio of 4-cycle-free planar graphs

Tom Kelly, Sid Kolichala, Caleb McFarland +1

We prove that every -vertex planar graph with no triangle sharing an edge with a 4-cycle has independence ratio for . This…

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 grap…

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…