This well-known open problem can be restated using crossing numbers: the degenerate crossing number, dcr(G), of G equals the smallest number k so that G has an ...
This led Pach and Tóth to introduce the degenerate crossing number: we allow drawings which are degenerate in the sense that more than two edges ...
His goal was to maximize the number of multiple crossings involving many edges. Let us call a degenerate crossing an m-fold crossing if it involves m edges.
[PDF] The Degenerate Crossing Number and Higher-Genus Embeddings
www.csun.edu › slides › Sept24-14...
G has a (nearly) degenerate drawing in the plane with at most gcr(G) degenerate crossings, and at most gcr(G) self-crossings on each edge. Page 13 ...
... The degenerate crossing number is defined by allowing more than two edges to intersect at the same point; several variants (one of which is also called the ...
The genus crossing number, gcr(G), of G equals the smallest number k so that G has an embedding in a surface with k crosscaps. The question then becomes whether ...
This well-known open problem can be restated using crossing numbers: the degenerate crossing number, $dcr(G)$, of $G$ equals the smallest number $k$ so that $G$ ...
The Degenerate Crossing Number and Higher-Genus. Embeddings. Suppose a graph can be embedded in a surface with k crosscaps. Is there always an embedding (in ...
Mar 4, 2022 · Discrete Applied Math Seminar By Marcus Schaefer: The Degenerate Crossing Number and Higher-Genus Embeddings. March 4, 2022. Time. 3:30pm - 4 ...
The Degenerate Crossing Number and Higher-Genus Embeddings. Marcus Schaefer. Can we quantify how much topology a graph embedded in a surface needs to use?