7 citations · 14 across the 7 of their papers we have counts for
8 papers
Improved Decomposition Bounds for Partition Polytopes and Odd-Covers
Steffen Borgwardt, Zdeněk Dvořák, Bryce Frederickson +2
The assignments of a set of items into clusters of prescribed sizes can be encoded as the vertices of the partition polytope . W…
Path Odd-Covers of Graphs
Steffen Borgwardt, Calum Buchanan, Eric Culver +3
We introduce and study "path odd-covers", a weakening of Gallai's path decomposition problem and a strengthening of the linear arboricity problem. The "path odd-cover number" $p_2(…
Sampling planar tanglegrams and pairs of disjoint triangulations
Alexander E. Black, Kevin Liu, Alex Mcdonough +4
A tanglegram consists of two rooted binary trees and a perfect matching between their leaves, and a planar tanglegram is one that admits a layout with no crossings. We show that th…
A unified Erdős-Pósa theorem for cycles in graphs labelled by multiple abelian groups
J. Pascal Gollin, Kevin Hendrey, O-joung Kwon +2
In 1965, Erdős and Pósa proved that there is an (approximate) duality between the maximum size of a packing of cycles and the minimum size of a vertex set hitting all cycles. Such…
Approximating TSP walks in subcubic graphs
Michael C. Wigal, Youngho Yoo, Xingxing Yu
We prove that every simple 2-connected subcubic graph on vertices with vertices of degree 2 has a TSP walk of length at most , confirming a conjecture…
Packing -paths of length zero modulo a prime
Robin Thomas, Youngho Yoo
It is known that -paths of length mod satisfy the Erdős-Pósa property if or , but not if is composite. We show that if is prime, then -paths of…
Packing cycles in undirected group-labelled graphs
Robin Thomas, Youngho Yoo
We prove a refinement of the flat wall theorem of Robertson and Seymour to undirected group-labelled graphs where assigns to each edge of an undirected graph an ele…
The extremal functions for triangle-free graphs with excluded minors
Robin Thomas, Youngho Yoo
We prove two results: 1. A graph on at least seven vertices with a vertex such that is planar and triangles satisfies . 2. For $p=2,…