On the width-length inequality

This paper was written at the Rensselaer Polytechnic Institute in 1963. A lecture based on it was given at the Rand Corporation in 1965 and this version is in the form in which Ray Fulkerson received it at Rand.The paper is the underpinning for results on resistor network inequalities (Reference [4]) which has not been published. A specific example, however, appears inProceedings of the IEEE 51 (1963) 1047–1048.More is known about minimal non-W—L matrices. U. Peled has found several additional classes of matrices which are also classically known in other contexts. A consequence of a recent matrix theorem is apparently that the degenerate projection planes are the only minimal matrices requiring unequal weights.