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Determine which of the graphs in Fig. 11.69 are planar. If a graph is planar, redraw it with noedges overlapping. If it is nonplanar, find a subgraph homeomorphic to either K5 or K3.Figure 11.69
Determine which of the graphs in Fig. 11.69 are planar. If a graph is planar, redraw it with noedges overlapping. If it is nonplanar, find a subgraph homeomorphic to either K5 or K3.Figure 11.69
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A planar graph G is outerplanar if G can be drawn in the plane so that all of its vertices lie on the exterior boundary. (i) Show that K4 and K2,3 are not outerplanar. (ii) Deduce that, if G is an outerplanar graph, then G contains no subgraph homeomorphic or contractible to K4 or K23. (The converse result also holds, yielding a Kuratowski-type criterion for a graph to be outerplanar.) | Numerade
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Determine which of the graphs in Fig. 11.69 are planar. If a graph is planar, redraw it with noedges overlapping. If it is nonplanar, find a subgraph homeomorphic to either K5 or K3.Figure 11.69
Determine which of the graphs in Fig. 11.69 are planar. If a graph is …
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A planar graph G is outerplanar if G can be drawn in the plane so that all of its vertices lie on the exterior boundary. (i) Show that K4 and K2,3 are not outerplanar. (ii) Deduce that, if G is an outerplanar graph, then G contains no subgraph homeomorphic or contractible to K4 or K23. (The converse result also holds, yielding a Kuratowski-type criterion for a graph to be outerplanar.) | Numerade
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