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Results tagged with topological-graph-theory
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user 56833
Graph theoretical questions with a topological flavour. For example, graphs on surfaces, spatial embeddings, and geometric graphs. Use the graph-drawing tag for questions specific to graph drawing (e.g. crossing numbers).
2
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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
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0
answers
97
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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
1
vote
0
answers
42
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What lower bounds are known for pair crossing number and related questions in multigraphs?
So in terms of crossing number https://arxiv.org/pdf/1808.10480 gives a lower bound of $O(e^{2.5}/n^{1.5})$ for multigraphs with no face of length 2 with no node contained inside.
What do we know abo …
- 111