5 citations · 32 across the 42 of their papers we have counts for
5 papers · 1 filter
Ubiquity in graphs III: Ubiquity of locally finite graphs with extensive tree-decompositions
Nathan Bowler, Christian Elbracht, Joshua Erde +4
A graph is said to be ubiquitous, if every graph that contains arbitrarily many disjoint -minors automatically contains infinitely many disjoint -minors. The well-kno…
Hamiltonian decompositions of 4-regular Cayley graphs of infinite abelian groups
Joshua Erde, Florian Lehner
A well-known conjecture of Alspach says that every -regular Cayley graph of an abelian group can be decomposed into Hamiltonian cycles. We consider an analogous question for in…
Planarity and genus of sparse random bipartite graphs
Tuan Anh Do, Joshua Erde, Mihyun Kang
The genus of the binomial random graph is well understood for a wide range of . Recently, the study of the genus of the random bipartite graph , with…
Large complete minors in random subgraphs
Joshua Erde, Mihyun Kang, Michael Krivelevich
Let be a graph of minimum degree at least and let be the random subgraph of obtained by keeping each edge independently with probability . We are interested in…
Enlarging vertex-flames in countable digraphs
Joshua Erde, J. Pascal Gollin, Attila Joó
A rooted digraph is a vertex-flame if for every vertex there is a set of internally disjoint directed paths from the root to whose set of terminal edges covers all ingoing…