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- W2126687412 abstract "We prove that, for every positive integer k , there is an integer N such that every 4-connected non-planar graph with at least N vertices has a minor isomorphic to K 4 , k , the graph obtained from a cycle of length 2 k + 1 by adding an edge joining every pair of vertices at distance exactly k , or the graph obtained from a cycle of length k by adding two vertices adjacent to each other and to every vertex on the cycle. We also prove a version of this for subdivisions rather than minors, and relax the connectivity to allow 3-cuts with one side planar and of bounded size. We deduce that for every integer k there are only finitely many 3-connected 2-crossing-critical graphs with no subdivision isomorphic to the graph obtained from a cycle of length 2 k by joining all pairs of diagonally opposite vertices." @default.
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- W2126687412 date "2011-03-01" @default.
- W2126687412 modified "2023-10-18" @default.
- W2126687412 title "Large non-planar graphs and an application to crossing-critical graphs" @default.
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- W2126687412 doi "https://doi.org/10.1016/j.jctb.2010.12.001" @default.
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