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It's obvious why any graph containing K(5) wouldn't be 4-colourable, but what about graphs containing only instances of K(3,3) to assert their non-planarity? (Edit: By a graph "containing" another graph, I mean having it as a subgraph. Sorry for being unclear.unclear. Although now that I think about it, perhaps the word "minor" is better.) |
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Are there any non-planar graphs containing only K(3,3) as a minor subgraph that are not 4-colourable?It's obvious why any graph containing K(5) wouldn't be 4-colourable, but what about graphs containing only instances of K(3,3) to assert their non-planarity? (Edit: By a graph "containing" another graph, I mean having it as a minorsubgraph. Sorry for being unclear.) |
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2 | clarification or what I mean by "containing".; deleted 3 characters in body; edited title | ||
Are there any non-planar graphs containing only K(3,3) as a minor that are not 4-colourable?It's obvious why any graph containing K(5) wouldn't be 4-colourable, but what about graphs containing only instances of K(3,3) to assert their non-planarity? (Edit: By a graph "containing" another graph, I mean having it as a minor. Sorry for being unclear.) |
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