A graph G is k-crossing-critical if cr ( G ) ≥ k and every proper subgraph H of G has cr ( H ) < k . The 1-crossing-critical graphs are exactly the Kuratowski ...
Jan 28, 2019 · The crossing number of a graph G is the least number of crossings over all possible drawings of G. We present a structural characterization of ...
The crossing number of a graph G is the least number of crossings over all possible drawings of G. We present a structural characterization of graphs with ...
We present a structural characterization of graphs with crossing number one. The crossing number of a graph G is the least number of crossings over all possible ...
Crossing number lemma - graph theory - Math Stack Exchange
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May 3, 2021 · For each edge f=uv that crosses an edge e, if there are not already edges from the endpoints of e to the endpoints of f, add them.
A graph is called 1-planar if it can be drawn in the plane so that each of its edges is crossed by at most one other edge. We show that every 1-planar drawing ...
Apr 18, 2022 · It is not possible that in an optimal drawing of a 1-planar graph, every edge is crossed. Here is a proof.
Dec 2, 2011 · You're done if you can show by case analysis that no matter how the edges are added, more than one crossing is created.
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In the mathematics of graph drawing, the crossing number inequality or crossing lemma gives a lower bound on the minimum number of edge crossings.
The crossing number of a graph G is the least number of crossings over all possible drawings of G. We present a structural characterization of graphs with ...