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
General position subsets ★★
Author(s): Gowers
Question What is the least integer such that every set of at least points in the plane contains collinear points or a subset of points in general position (no three collinear)?
Colouring $d$-degenerate graphs with large girth ★★
Author(s): Wood
Question Does there exist a -degenerate graph with chromatic number and girth , for all and ?
Keywords: degenerate; girth
Forcing a 2-regular minor ★★
Conjecture Every graph with average degree at least contains every 2-regular graph on vertices as a minor.
Keywords: minors