Kt Minors in Large t-Connected Graphs
نویسنده
چکیده
It appears that for t ≥ 6 the structure of large (t− 1)-connected graphs with no Kt minor is prohibitively complicated. Moreover, for t ≥ 8 the assumption in the above conjecture that |V (G)| is large is also necessary. In fact, Thomason has shown that there exist Θ(t √ log t)-connected graphs with no Kt-minor, but all known examples are bounded in size by a function of t. Thus, the conditions imposed on the connectivity and the size of the graph can not be relaxed. In 2005 DeVos, Kawarabayashi, Thomas, Wollan and I verified this conjecture for t ≤ 6. Recently, Thomas and I verified it for t ≤ 8. We continue working on the general case.
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