The planar graph product structure theorem of Dujmović et al.[J. ACM, 67 (2020), 22] states
that every planar graph is a subgraph of the strong product of a graph with bounded …

Product structure of graph classes with bounded treewidth Page 1 Combinatorics, Probability
and Computing (2023), 1–26 doi:10.1017/S0963548323000457 ARTICLE Product structure of …

This paper shows that $ K_t $-minor-free (and $ K_ {s, t} $-minor-free) graphs $ G $ are
subgraphs of products of a tree-like graph $ H $(of bounded treewidth) and a complete …

Dujmovic, Joret, Micek, Morin, Ueckerdt and Wood [J. ACM 2020] proved that for every
graph G with Euler genus g there is a graph H with treewidth at most 4 and a path P such …

We study the two-player communication problem of determining whether two vertices $ x, y $
are nearby in a graph $ G $, with the goal of determining the graph structures that allow the …

This paper explores the structure of graphs defined by an excluded minor or an excluded
odd minor through the lens of graph products and tree-decompositions. We prove that every …

A graph U is universal for a graph class C∋ U, if every G∈ C is a minor of U. We prove the
existence or absence of universal graphs in several natural graph classes, including graphs …

Abstract Dujmovć, Joret, Micek, Morin, Ueckerdt, and Wood established that every planar
graph is a subgraph of the strong product of a graph with bounded treewidth and a path …

A squaregraph is a plane graph in which each internal face is a 4‐cycle and each internal
vertex has degree at least 4. This paper proves that every squaregraph is isomorphic to a …

A graph class $\mathcal {G} $ has linear growth if, for each graph $ G\in\mathcal {G} $ and
every positive integer $ r $, every subgraph of $ G $ with radius at most $ r $ contains $ O (r) …