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Minors
Highly connected graphs with no K_n minor ★★★
Author(s): Thomas
Problem Is it true for all
, that every sufficiently large
-connected graph without a
minor has a set of
vertices whose deletion results in a planar graph?
![$ n \ge 0 $](/files/tex/90df48fa9e1e2158a5da469f1fb382d91bf47483.png)
![$ n $](/files/tex/ec63d7020a64c039d5f6703b8fa3ab7393358b5b.png)
![$ K_n $](/files/tex/3047d5de14f4534bc7c4d3e1d86c3fb292aea727.png)
![$ n-5 $](/files/tex/9ed6ca429bf7a035c85bba441d0e1299c0af67dc.png)
Keywords: connectivity; minor
Seagull problem ★★★
Author(s): Seymour
Conjecture Every
vertex graph with no independent set of size
has a complete graph on
vertices as a minor.
![$ n $](/files/tex/ec63d7020a64c039d5f6703b8fa3ab7393358b5b.png)
![$ 3 $](/files/tex/4aaf85facb6534fd470edd32dbdb4e28f6218190.png)
![$ \ge \frac{n}{2} $](/files/tex/4efffa1e5aca5aa0354077be96157068fab5f8be.png)
Keywords: coloring; complete graph; minor
Forcing a $K_6$-minor ★★
Author(s): Barát ; Joret; Wood
Conjecture Every graph with minimum degree at least 7 contains a
-minor.
![$ K_6 $](/files/tex/ba39f6d33baf4500a21bc1905745d7c0414444e6.png)
Conjecture Every 7-connected graph contains a
-minor.
![$ K_6 $](/files/tex/ba39f6d33baf4500a21bc1905745d7c0414444e6.png)
Keywords: connectivity; graph minors
Forcing a 2-regular minor ★★
Conjecture Every graph with average degree at least
contains every 2-regular graph on
vertices as a minor.
![$ \frac{4}{3}t-2 $](/files/tex/e3058b3a3212b3db0404690975e13ff4036eafd0.png)
![$ t $](/files/tex/4761b031c89840e8cd2cda5b53fbc90c308530f3.png)
Keywords: minors
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