2017/03/10 by Erde, Joshua
#Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.1703.03756
There are many results asserting the existence of tree-decompositions of minimal width which still represent local connectivity properties of the underlying graph, perhaps the best-known being Thomas' theorem that proves for every graph G the existence of a linked tree-decompositon of width tw(G). We prove a general theorem on the existence of linked and lean tree-decompositions, providing a unifying proof of many known results in the field, as well as implying some new results. In particular we prove that every matroid M admits a lean tree-decomposition of width tw(M), generalizing the result of Thomas.