We present and prove several results concerning the length of longest cycles in 2-connected or I-tough graphs with large degree sums. These results improve many known results on long cycles in these graphs. We also consider the sharpness of the results and discuss some possible strengthenings. 0 1996 John Wiley & Sons, Inc.
i = 1,2). The result generalizes a known characterization of bipartite graphs with a k-factor. Its proof uses flow theory and is a refinement of the proof of an analogous result due to Folkman and Fulkerson. By applying corresponding flow algorithms, the described decomposition can be found in polynomial time if it exists. As an application, an assignment problem is solved. o 7993 by ~o h n wi/ey & Sons, Inc.
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