Abstract
A simple algorithm is developed which allows to decide whether or not a given hexagonal system has a perfect matching (and to find such a matching). This decision is also of chemical relevance since a hexagonal system is the skeleton of a benzenoid hydrocarbon molecule if and only if it has a perfect matching.
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References
F. Harary, The cell growth problem and its attempted solutions,Beiträge zur Graphentheorie (Int. Koll. Manebach, 9–12. Mai 1967), ed. H. Sachs, H.—J. Voss, and H. Walther. B. G. Teubner Verlagsgesellschaft Leipzig 1968, 49–60.
J. E. Hopcroft andR. M. Karp, An 5/2 algorithm for maximum matchings in bipartite graphs,SIAM J. Comput. 2 (1973) 225–231.
E. L. Lawler,Combinatorial Optimization: Networks and Matroids, Holt, Rinehart and Winston, New York, 1976.
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Dedicated to Paul Erdős on his seventieth birthday
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Sachs, H. Perfect matchings in hexagonal systems. Combinatorica 4, 89–99 (1984). https://doi.org/10.1007/BF02579161
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DOI: https://doi.org/10.1007/BF02579161