Years and Authors of Summarized Original Work
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2011; Grohe, Kawarabayashi, Marx, Wollan
Problem Definition
To subdivide an edge e in a graph G with endpoints u and v, delete the edge from the graph and add a path of length two connecting the vertices u and v. A graph G is a subdivision of graph H if G can be obtained from H by repeatedly subdividing edges. A graph H is a topological subgraph (or topological minor) of graph G if a subdivision of H is a subgraph of G. Equivalently, H is a topological subgraph of G if H can be obtained from G by deleting edges, deleting vertices, and suppressing vertices of degree 2 (to suppress a vertex of degree 2, delete the vertex and add an edge connecting its two neighbors). The notion of topological subgraphs appears in the classical result of Kuratowski in 1935 stating that a graph is planar if and only if it does not have a topological subgraph isomorphic to K5 or K3, 3. This entry considers the problem of determining, given a graph G and H,...
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Wollan, P. (2016). Finding Topological Subgraphs. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-2864-4_695
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