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Network Flows, Minimum Coverings, and the Four-Color Conjectures

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  • David B. Weinberger

    (Bell Laboratories, Holmdel, New Jersey)

Abstract

In this paper we use Fulkerson's antiblocking theory as a framework in which to explore certain combinatorial properties of network flows. In particular, we derive a surprising round-off result for a class of integer covering problems. When combined with Edmond's characterization of the matching polytope, our results yield an interesting proposition concerning the four-color conjecture. Our goal in presenting this proposition is not so much to propose a new approach to the famous conjecture as it is to present an interesting example of the interrelation of a number of seemingly diverse areas of combinatorics and combinatorial optimization—in particular, antiblocking and minimum coverings, integer network flows, edge matchings in graphs, and graph coloring.

Suggested Citation

  • David B. Weinberger, 1976. "Network Flows, Minimum Coverings, and the Four-Color Conjectures," Operations Research, INFORMS, vol. 24(2), pages 272-290, April.
    • Handle: RePEc:inm:oropre:v:24:y:1976:i:2:p:272-290
    DOI: 10.1287/opre.24.2.272
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