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Tagged with planar-graphs graph-minors
3 questions
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Is there is a constant $c$ such that toroidal graphs are minor-$c$-colorable?
A toroidal graph is a graph that can be embedded on a torus. In other words, the graph's vertices can be placed on a torus such that no edges cross.
A minor of graph G is a graph obtained from G by ...
6
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Does every $4$-connected nonplanar graph contain a $K_5$-minor?
By Kuratowski's theorem, every nonplanar graph contains a (topological) minor of $K_5$ or $K_{3,3}$.
But I observed that every time I construct a $4$-connected nonplanar graph, it always contains not ...
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Mac Lane-like condition for intrinsically linked graphs?
If any embedding of your graph in 3-space has two cycles that are linked, then your graph is intrinsically linked (such as the Petersen graph). These graphs generalise non-planar graphs since for ...