Abstract The determination of the currents and voltages in a countably infinite electrical network containing infinite energy requires not only the imposition of Kirchoff's laws and Ohm's laws but also the arbitrary assignment of the current‐voltage pairs in certain sets of branches, called joints. For finitely chainlike, countably infinite networks the maximal joint sets satisfy the base axioms of a matroid.

An undirected graph G is called a circular-arc graph if there exists a family of arcs on a circle and a 1–1 correspondence between vertices and arcs such that two distinct vertices are adjacent if and only if the corresponding arcs overlap. Such a family is called a circular-arc model for G. In this paper we present an $O(n)^3 $-step algorithm for testing whether an n-vertex graph is a circular-arc graph, and if it is, constructing a circular-arc model. Unfortunately the algorithm, its proof, and its efficient implementation are all quite involved.