On Median Graphs and Median Grid Graphs on Median Graphs and Median Grid Graphs
نویسنده
چکیده
Let e be an edge of a median graph G which is contained in exactly one 4-cycle. Then it is proved that G n e is a median graph. The converse holds as well provided that e is not contained is a subgraph isomorphic to the 3-cube minus a vertex. These results are used to give several characterizations of median grid graphs. (Grid graphs are subgraphs of complete grids, i.e. of the Cartesian product of paths.) The length of the outer face of a plane median grid graph is expressed with the number of equivalence classes of a certain relation. Retracts of complete grids are also brieey discussed and two characterizations of median graphs are given.
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