3 citations · 8 across the 14 of their papers we have counts for
8 papers · 1 filter
Asymptotic structure. II. Path-width and additive quasi-isometry
Tung Nguyen, Alex Scott, Paul Seymour
We show that if a graph admits a quasi-isometry to a graph of bounded path-width, then we can assign a non-negative integer length to each edge of , such that the sa…
Line-width and path-width
Tung Nguyen, Alex Scott, Paul Seymour
For finite graphs, path-width is an interesting and useful concept, but if we extend it to infinite graphs in the most obvious way (by making the indexing path infinite), it does n…
Asymptotic structure. VI. Distant paths across a disc
Tung Nguyen, Alex Scott, Paul Seymour
Menger's theorem says that, for , if are sets of vertices in a graph , then either there are vertex-disjoint paths between and , or there is a set X…
Asymptotic structure. III. Excluding a fat tree
Tung Nguyen, Alex Scott, Paul Seymour
Robertson and Seymour proved that for every finite tree , there exists such that every finite graph with no minor has path-width at most ; and conversely, for eve…
Asymptotic structure. V. The coarse Menger conjecture in bounded path-width
Alex Divoux, Tung Nguyen, Alex Scott +1
Menger's theorem tells us that if are sets of vertices in a graph , then (for ) either there are vertex-disjoint paths between and , or there is a set…
Asymptotic structure. IV. A counterexample to the weak coarse Menger conjecture
Tung Nguyen, Alex Scott, Paul Seymour
Coarse graph theory concerns finding 'coarse' analogues of graph theory theorems, replacing disjointness with being far apart. One of the most interesting open questions is to find…
The vertex sets of subtrees of a tree
Maria Chudnovsky, Tung Nguyen, Alex Scott +1
Let be a set of subsets of a set . When is there a tree with vertex set such that each member of is the set of vertices of a subtree of ?…
Asymptotic structure. I. Coarse tree-width
Tung Nguyen, Alex Scott, Paul Seymour
In this paper, we develop a coarse analogue of tree-width. We prove that a graph admits a tree-decomposition in which each bag is contained in the union of a bounded number of…