Characterizing multiloop topologies is an important step towards developing
novel methods at high perturbative orders in quantum field theory. In this
article, we exploit the Loop-Tree Duality (LTD) formalism to analyse multiloop
topologies that appear for the first time at five loops. Explicitly, we open
the loops into connected trees and group them according to their topological
properties. Then, we identify a kernel generator, the so-called N7MLT
universal topology, that allow us to describe any scattering amplitude of up to
five loops. Furthermore, we provide factorization and recursion relations that
enable us to write these multiloop topologies in terms of simpler
subtopologies, including several subsets of Feynman diagrams with an arbitrary
number of loops. Our approach takes advantage of many symmetries present in the
graphical description of the original fundamental five-loop topologies. The
results obtained in this article might shed light into a more efficient
determination of higher-order corrections to the running couplings, which are
crucial in the current and future precision physics program.Comment: 14 pages, 6 figures, 2 table