Flexibly Planar and Flexibly Flat Graphs
نویسندگان
چکیده
We say a graph G is flexibly planar if and only if for every cycle in G, there exists a planar embedding of G such that the cycle bounds a disk whose interior is disjoint from G. We show the complete minor-minimal set of flexibly planar graphs is the single graph K4 We further investigate the property of flexible flatness, a property that has an analogous definition for 3space. We show, with one exception, that a Petersen family graph, P , with one edge removed, is not flexibly flat. We also show that flexible flatness is preserved by neither minors nor by ∆− Y nor Y −∆ exchanges.
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