2023/11/22 by Kelly, Samuel
#FOS: Mathematics #Group Theory (math.GR) #Metric Geometry (math.MG)
paper · doi:10.48550/arxiv.2311.13195
We prove that for any finite tree T with n vertices and maximal degree 3, there is a topological embedding of T into the integer grid Z2 which maps vertices to vertices and whose image meets at most (7)/(3)n vertices. This recovers a weaker form of a result due to Valiant 10.5555/1963635.1963641 with stronger constants. We address question 7.7 of arXiv:2112.05305, giving the first example of a pair of graphs X,Y such that there is no regular map X→ Y but the coarse wiring profile of X into Y grows linearly.