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with the graph's vertices in a line along the spine of the book. Its edges are drawn on separate pages in such a way that edges residing on the same page do not cross. This problem abstracts layout problems arising in the routing of multilayer printed circuit boards.
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of a graph in time linear to the number of edges. Their algorithm does this by constructing a graph embedding which they term a "palm tree". Efficient planarity testing is fundamental to
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This article is about the study of graph embeddings. For graphs in the plane with crossings, see
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with a single-element set per vertex and a two-element set per edge. The geometric realization |
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glued together at vertices. In this view, embeddings of graphs into a surface or as
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Embedding a graph in a surface means that we want to draw the graph on a surface, a
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495:"Embedding Graphs in Books: A Layout Problem with Applications to VLSI Design"
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109:(the surface) without two connections crossing each other and resulting in a
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of the graph (equivalently, the clique complex of the complement of the
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Other simplicial complexes associated with graphs include the
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of other graphs are both instances of topological embedding,
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where the aim is to print (embed) a circuit (the graph) on a
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intersecting. A basic embedding problem often presented as a
370:"Torsion in the matching complex and chessboard complex"
16:Branch of the mathematical field of graph theory
503:SIAM Journal on Algebraic and Discrete Methods
101:. Other applications can be found in printing
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146:| of the complex consists of a copy of the
162:is just the specialization of topological
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38:Animation detailing the embedding of the
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150:per edge, with the endpoints of these
266:structural results about graphs, via
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42:and associated map in the torus
284:Crossing number (graph theory)
1:
432:"Efficient planarity testing"
253:embedding a graph into a book
251:et al studied the problem of
212:). The matching complex of a
174:, and a connected graph is a
117:Graphs as topological spaces
68:spatial embeddings of graphs
137:abstract simplicial complex
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409:10.1016/j.aim.2006.10.014
309:Topological combinatorics
172:topological connectedness
89:for example, without two
536:Topological graph theory
340:Topological Graph Theory
214:complete bipartite graph
52:topological graph theory
375:Advances in Mathematics
272:graph structure theorem
160:homeomorphism of graphs
99:three utilities problem
200:of the graph, and the
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451:10.1145/321850.321852
239:testing the planarity
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135:we may associate an
237:derived a means of
103:electronic circuits
95:mathematical puzzle
60:embedding of graphs
439:Journal of the ACM
366:Wachs, Michelle L.
364:Shareshian, John;
268:graph minor theory
219:chessboard complex
166:, the notion of a
78:. It also studies
76:topological spaces
44:
428:Tarjan, Robert E.
350:978-0-486-41741-7
262:are also used to
204:, with a set per
196:, with a set per
183:fundamental group
58:. It studies the
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21:topological graph
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491:Rosenberg, A. L.
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260:Graph embeddings
202:matching complex
133:undirected graph
123:Graph (topology)
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516:10.1137/0608002
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487:Leighton, F. T.
483:Chung, F. R. K.
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399:10.1.1.499.1516
389:math.CO/0409054
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226:Example studies
190:Whitney complex
170:coincides with
168:connected graph
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445:(4): 549–568.
424:Hopcroft, John
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382:(2): 525–570.
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304:Toroidal graph
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194:clique complex
179:if and only if
127:Graph homology
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510:(1): 33–58.
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335:Tucker, T.W.
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294:Planar graph
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216:is called a
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185:is trivial.
156:subdivisions
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56:graph theory
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40:Pappus graph
82:of graphs.
48:mathematics
210:line graph
121:See also:
80:immersions
460:1813/6011
394:CiteSeerX
368:(2007) .
343:. Dover.
337:(2012) .
299:Real tree
249:Fan Chung
152:intervals
530:Category
493:(1987).
430:(1974).
278:See also
270:and the
206:matching
64:surfaces
469:6279825
97:is the
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198:clique
131:To an
87:sphere
72:graphs
70:, and
498:(PDF)
465:S2CID
435:(PDF)
384:arXiv
320:Notes
289:Genus
264:prove
91:edges
345:ISBN
233:and
181:its
176:tree
125:and
512:doi
455:hdl
447:doi
404:doi
380:212
192:or
74:as
62:in
46:In
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