A note on 3-choosability of planar graphs
In this note, we prove that a planar graph is 3-choosable if it contains neither cycles of length 4, 7, and 9 nor 6-cycle with one chord. In particular, every planar graph without cycles of length 4, 6, 7, or 9 is 3-choosable. Together with other known parallel results, this completes a theorem on 3-choosability of planar graphs: planar graphs without cycles of length 4, i, j, 9 with i < j and i, j E 15, 6, 7, 8) are 3-choosable. Moreover, some further problems on this direction are proposed. (c) 2007 Published by Elsevier B.V.
planar graph cycle combinatorial problems choosability