The Complexity of Several Realizability Problems for Abstract Topological Graphs
نویسنده
چکیده
topological graph (AT-graph): A = (G, R); G = (V, E) is a graph, R ⊆ ( E 2 ) in a topological graph T ... RT = set of crossing pairs of edges AT-graph A is realizable if there exists a topological graph T which is a drawing of G and RT = R. simply realizable ... T is simple rectilinearly realizable ... edges of T are straight-line segments weakly realizable ... RT ⊆ R Abstract topological graph (AT-graph): A = (G, R); G = (V, E) is a graph, R ⊆ ( E 2 )topological graph (AT-graph): A = (G, R); G = (V, E) is a graph, R ⊆ ( E 2 ) in a topological graph T ... RT = set of crossing pairs of edges AT-graph A is realizable if there exists a topological graph T which is a drawing of G and RT = R. simply realizable ... T is simple rectilinearly realizable ... edges of T are straight-line segments weakly realizable ... RT ⊆ R Abstract topological graph (AT-graph): A = (G, R); G = (V, E) is a graph, R ⊆ ( E 2 )topological graph (AT-graph): A = (G, R); G = (V, E) is a graph, R ⊆ ( E 2 ) in a topological graph T ... RT = set of crossing pairs of edges AT-graph A is realizable if there exists a topological graph T which is a drawing of G and RT = R. simply realizable ... T is simple rectilinearly realizable ... edges of T are straight-line segments weakly realizable ... RT ⊆ R Abstract topological graph (AT-graph): A = (G, R); G = (V, E) is a graph, R ⊆ ( E 2 )topological graph (AT-graph): A = (G, R); G = (V, E) is a graph, R ⊆ ( E 2 ) in a topological graph T ... RT = set of crossing pairs of edges AT-graph A is realizable if there exists a topological graph T which is a drawing of G and RT = R. simply realizable ... T is simple rectilinearly realizable ... edges of T are straight-line segments weakly realizable ... RT ⊆ R Abstract topological graph (AT-graph): A = (G, R); G = (V, E) is a graph, R ⊆ ( E 2 )topological graph (AT-graph): A = (G, R); G = (V, E) is a graph, R ⊆ ( E 2 ) in a topological graph T ... RT = set of crossing pairs of edges AT-graph A is realizable if there exists a topological graph T which is a drawing of G and RT = R. simply realizable ... T is simple rectilinearly realizable ... edges of T are straight-line segments weakly realizable ... RT ⊆ R Abstract topological graph (AT-graph): A = (G, R); G = (V, E) is a graph, R ⊆ ( E 2 )topological graph (AT-graph): A = (G, R); G = (V, E) is a graph, R ⊆ ( E 2 ) in a topological graph T ... RT = set of crossing pairs of edges AT-graph A is realizable if there exists a topological graph T which is a drawing of G and RT = R. simply realizable ... T is simple rectilinearly realizable ... edges of T are straight-line segments weakly realizable ... RT ⊆ R Example: A = (K4, {{{1, 3}, {2, 4}}})
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