Alternating Euler Paths for Packings and Covers

Work supported by Department of Energy contract DE–AC02–76SF00515.puter Department, and presently with the Computation Group of the Stanford Linear Accelerator Center. He is a member of the MAA and the ACM, and his main research interest is picture processing and pattern recognition. Editor. 1. Introduction. An interesting combinatorial problem known as the "school-girls' walk" asks if the girls in an all-girl school can take a walk in two-by-two fashion so that each pair walking side by side are on friendly terms, it being known which pairs are friendly among all possible pairings. If such a utopian arrangement is not possible, then what is the largest number of friendly pairings that can be achieved simultaneously and how can such an optimal set of pairings be found? This problem is qbstractly equivalent to a problem in graph theory which is as

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