Edge colorings in bipartite graphs

Jon H. Folkman

ResearchPublished 1966

The determination of conditions for color-feasibility of a list of nonnegative integers, P, in a bipartite graph, G. Necesssary and sufficient conditions are obtained in case the n-list P contains at most two distinct positive integers. It is shown that these conditions (while necessary in the general case) are not sufficient if P contains three or more distinct positive integers. For the case of two distinct integers in P, the method of proof leads to an efficient edge-coloring algorithm. The main results can also be interpreted in terms of sum decompositions of (0, 1)-matrices or in terms of multicommodity flows in certain kinds of connected networks.

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Folkman, Jon H., Edge colorings in bipartite graphs. Santa Monica, CA: RAND Corporation, 1966. https://www.rand.org/pubs/research_memoranda/RM5061.html.
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