@Jon Yard, @Deane Yang, wasn't there a turf battle between mathematics and electrical engineering for "ownership" or "rights" to computer science and information theory. At some places, computer science is a part or division of Electrical Engineering. At few, computer science is a branch of mathematics. And at many places, it is a department in its own right. The same thing happens with Neurosurgery. Some schools have Divisions of Neurosurgery as part of the Department of Surgery, others free-standing Depts of Neurosurgery, and for some odd ducks it's part of Neurology, a medical branch.

@Barbara, (sadly), obtaining funding for a lab is considered valid criteria for claiming authorship according to the American Medical Association. See my comment below regarding their authorship form requirements.

Is the spanning tree $T$ a given at the beginning of this problem, or is it a part of the problem to also find the spanning tree?