A decomposition of locally finite graphs
We prove that every infinite, connected, locally finite graph G can be expressed as an edge-disjoint union of a leafless tree T, rooted at an arbitrarily chosen vertex of G, and a collection of finite graphs H1, H2, H3,...such that, for all i less than j, the vertices common to Hi and Hj lie in T, and no vertex of Hj lies on T between a vertex of Hi∩T and the root. © 1993.
Publication Source (Journal or Book title)
Oporowski, B. (1993). A decomposition of locally finite graphs. Discrete Mathematics, 117 (1-3), 161-168. https://doi.org/10.1016/0012-365X(93)90332-N