47 citations · 678 across the 85 of their papers we have counts for
5 papers · 1 filter
A chain theorem for sequentially -rank-connected graphs with respect to vertex-minors
Duksang Lee, Sang-il Oum
Tutte (1961) proved the chain theorem for simple -connected graphs with respect to minors, which states that every simple -connected graph has a simple -connected mino…
Bounds for the Twin-width of Graphs
Jungho Ahn, Kevin Hendrey, Donggyu Kim +1
Bonnet, Kim, Thomassé, and Watrigant (2020) introduced the twin-width of a graph. We show that the twin-width of an -vertex graph is less than $(n+\sqrt{n\ln n}+\sqrt{n}+2\ln n)…
Obstructions for matroids of path-width at most k and graphs of linear rank-width at most k
Mamadou Mostapha Kanté, Eun Jung Kim, O-joung Kwon +1
Every minor-closed class of matroids of bounded branch-width can be characterized by a list of excluded minors, but unlike graphs, this list may need to be infinite in general. How…
Intertwining connectivities for vertex-minors and pivot-minors
Duksang Lee, Sang-il Oum
We show that for pairs and of disjoint subsets of vertices of a graph , if is sufficiently large, then there exists a vertex in $V(G)-(Q\cup R\cup S\cup…
A unified half-integral Erdős-Pósa theorem for cycles in graphs labelled by multiple abelian groups
J. Pascal Gollin, Kevin Hendrey, Ken-ichi Kawarabayashi +2
Erdős and Pósa proved in 1965 that there is a duality between the maximum size of a packing of cycles and the minimum size of a vertex set hitting all cycles. Such a duality does n…