We prove that every sufficiently large 6-connected graph of bounded tree-width either has a K6 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 large 6-connected graphs. Jørgensen conjectured that it holds for all 6-connected graphs.
K6minors in 6-connected graphs of bounded tree-width / Kawarabayashi, Ken-ichi; Norine, Serguei; Thomas, Robin; Wollan, Paul. - In: JOURNAL OF COMBINATORIAL THEORY. - ISSN 0095-8956. - STAMPA. - (2017). [10.1016/j.jctb.2017.08.006]
K6minors in 6-connected graphs of bounded tree-width
Wollan, Paul
2017
Abstract
We prove that every sufficiently large 6-connected graph of bounded tree-width either has a K6 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 large 6-connected graphs. Jørgensen conjectured that it holds for all 6-connected graphs.File allegati a questo prodotto
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