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Article

Keywords:
elementary edge-cut; hexagonal system; perfect matching; plane bipartite graph
Summary:
We give a necessary and sufficient condition for the existence of perfect matchings in a plane bipartite graph in terms of elementary edge-cut, which extends the result for the existence of perfect matchings in a hexagonal system given in the paper of F. Zhang, R. Chen and X. Guo (1985).
References:
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[2] Hall, P.: On representatives of subsets. J. London Math. Soc. 10 (1935), 26-30. MR 0771431 | Zbl 0010.34503
[3] Sachs, H.: Perfect matchings in hexagonal systems. Combinatorica 4 (1984), 89-99. DOI 10.1007/BF02579161 | MR 0739417 | Zbl 0542.05048
[4] Zhang, F., Chen, R., Guo, X.: Perfect matchings in hexagonal systems. Graphs and Combinatorics 1 (1985), 383-386. DOI 10.1007/BF02582965 | MR 0951028 | Zbl 0614.05043
[5] Zhang, H., Zhang, F.: Plane elementary bipartite graphs. Discrete Appl. Math. 105 (2000), 291-311. DOI 10.1016/S0166-218X(00)00204-3 | MR 1780476 | Zbl 0957.05085
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