Planar Graph Embedding with fixed vertex positions
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Given a planar graph, and an arbitrary prescription for its vertex positions in in the plane. Can you always draw the edges of the graph without crossings (not straight segments, of course) for any given vertex positions?
I guess it is a bit like asking whether there is always a bijective transformation between embeddings of the same graph, because this can be posed as a deformation problem from the canonical straight-edge embedding.
planar-graph
asked Dec 19 '18 at 10:08
Amir VaxmanAmir Vaxman
988
$endgroup$
add a comment |
$begingroup$
Given a planar graph, and an arbitrary prescription for its vertex positions in in the plane. Can you always draw the edges of the graph without crossings (not straight segments, of course) for any given vertex positions?
I guess it is a bit like asking whether there is always a bijective transformation between embeddings of the same graph, because this can be posed as a deformation problem from the canonical straight-edge embedding.
planar-graph
asked Dec 19 '18 at 10:08
Amir VaxmanAmir Vaxman
988
$endgroup$
add a comment |
$begingroup$
Given a planar graph, and an arbitrary prescription for its vertex positions in in the plane. Can you always draw the edges of the graph without crossings (not straight segments, of course) for any given vertex positions?
I guess it is a bit like asking whether there is always a bijective transformation between embeddings of the same graph, because this can be posed as a deformation problem from the canonical straight-edge embedding.
planar-graph
asked Dec 19 '18 at 10:08
Amir VaxmanAmir Vaxman
988
$endgroup$
Given a planar graph, and an arbitrary prescription for its vertex positions in in the plane. Can you always draw the edges of the graph without crossings (not straight segments, of course) for any given vertex positions?
I guess it is a bit like asking whether there is always a bijective transformation between embeddings of the same graph, because this can be posed as a deformation problem from the canonical straight-edge embedding.
planar-graph
planar-graph
asked Dec 19 '18 at 10:08
Amir VaxmanAmir Vaxman
988
asked Dec 19 '18 at 10:08
Amir VaxmanAmir Vaxman
988
asked Dec 19 '18 at 10:08
Amir VaxmanAmir Vaxman
988
asked Dec 19 '18 at 10:08
Amir VaxmanAmir Vaxman
988
asked Dec 19 '18 at 10:08
Amir VaxmanAmir Vaxman
988
988
add a comment |
add a comment |
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