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arxiv: 1203.2171 · v2 · submitted 2012-03-09 · 🧮 math.CO · cs.DM

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K₆ minors in 6-connected graphs of bounded tree-width

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classification 🧮 math.CO cs.DM
keywords connectedgraphsboundedgraphholdssufficientlytree-widthconclusion
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We prove that every sufficiently big 6-connected graph of bounded tree-width either has a K_6 minor, or has a vertex whose deletion makes the graph planar. This is a step toward proving that the same conclusion holds for all sufficiently big 6-connected graphs. Jorgensen conjectured that it holds for all 6-connected graphs.

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