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We consider the problem of performing an edge coloring of a d-regular bipartite multigraph G = (V, E). While an edge coloring can be found by repeatedly performing Euler partitions on G, doing so requires that the degree of G be a power of 2. One way to allow the Euler partitioning method to continue in cases where d is not a power of 2 is to remove a perfect matching from the graph after any partition that results in a graph with an odd degree. If this perfect matching can be identified in O(E) time, we can maintain the best case runtime for this coloring of O(E lg d). This paper presents Chain Match, an algorithm that finds a perfect matching in a d-regular bipartite multigraph. While we have proven that Chain Match will always terminate with a perfect matching, we have not been able to implement it within our goal runtime of O(E).
Senior Honors Thesis. Advisor: Tom Cormen.
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Stefanie L. Ostrowski, "Chain Match: An Algorithm for Finding a Perfect Matching of a Regular Bipartite Multigraph." Dartmouth Computer Science Technical Report TR2014-753, May 2014.
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