Graph Theory » Coloring » Vertex coloring

Nonrepetitive colourings of planar graphs ★★

Author(s): Alon N.; Grytczuk J.; Hałuszczak M.; Riordan O.

Question   Do planar graphs have bounded nonrepetitive chromatic number?

Keywords: nonrepetitive colouring; planar graphs

Posted by David Wood
updated March 24th, 2014
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Geometry

General position subsets ★★

Author(s): Gowers

Question   What is the least integer $ f(n) $ such that every set of at least $ f(n) $ points in the plane contains $ n $ collinear points or a subset of $ n $ points in general position (no three collinear)?

Keywords: general position subset, no-three-in-line problem

Posted by David Wood
updated March 24th, 2014
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Graph Theory » Coloring

Colouring $d$-degenerate graphs with large girth ★★

Author(s): Wood

Question   Does there exist a $ d $-degenerate graph with chromatic number $ d + 1 $ and girth $ g $, for all $ d \geq 2 $ and $ g \geq 3 $?

Keywords: degenerate; girth

Posted by David Wood
updated March 16th, 2014
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Graph Theory » Basic G.T. » Minors

Forcing a 2-regular minor ★★

Author(s): Reed; Wood

Conjecture   Every graph with average degree at least $ \frac{4}{3}t-2 $ contains every 2-regular graph on $ t $ vertices as a minor.

Keywords: minors

Posted by David Wood
updated March 16th, 2014
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