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Results tagged with planar-graphs
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user 56833
graphs that can be embedded into the plane, i.e. that can be drawn without crossings between the lines representing edges.
4
votes
0
answers
137
views
Can the vertices of a planar graph of min degree 3 be covered with edges of average weight (...
Consider a planar graph where every vertex is incident to at least 3 edges, and assign to each edge a weight equal to the sum of the degrees of its endpoints.
If not, what is the smallest n so that e …
- 111
2
votes
1
answer
95
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Dipping into sets of parallel edges in graph drawings
Given a multigraph embedded in the plane call a maximal set of parallel edges between $u,v$ such that only one of the induced faces contains nodes besides $u$ or $v$ a topologically parallel set (tell …
- 111
1
vote
0
answers
77
views
Is there a variant of the crossing lemma for multigraphs with arbitrary embedding?
Suppose $G$ is a graph embedded in the plane with $m=|E(G)|$ edges and $n=|V(G)|$ vertices.
Suppose $\operatorname{sim}(G)$, the simplification of $G$ contains $ m' \gg 3n $ edges.
Call the set of edg …
- 111
1
vote
0
answers
97
views
Problem related to crossing number
Let $G$ be a graph embedded in the plane (with crossings). For $ F \subset E(G) $, denote by $c(F)$ the set of edges of $G$ that cross some edge in $F$.
Denote $\delta(v)$ the set of edges with one e …
- 111