Generalizations of critical connectivity of graphs
Discrete Mathematics - First Japan Conference on Graph Theory and Applications
List colourings of planar graphs
Discrete Mathematics
Every planar graph is 5-choosable
Journal of Combinatorial Theory Series B
Journal of Combinatorial Theory Series B - Special issue: dedicated to Professor W. T. Tutte on the occasion of his eightieth birthday
Choosability of K5-minor-free graphs
Discrete Mathematics
A relaxed Hadwiger's Conjecture for list colorings
Journal of Combinatorial Theory Series B
Extremal results for rooted minor problems
Journal of Graph Theory
Extremal functions for rooted minors
Journal of Graph Theory
Contractibility and the Hadwiger Conjecture
European Journal of Combinatorics
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Thomassen (J. Combin. Theory Ser. B, 62 (1994), pp. 180-181) proved that every planar graph is 5-choosable. This result was generalized by Škrekovski (Discrete Math., 190 (1998), pp. 223-226) and He, Miao, and Shen (Discrete Math., 308 (2008), pp. 4024-4026), who proved that every $K_5$-minor-free graph is 5-choosable. Both proofs rely on the characterization of $K_5$-minor-free graphs due to Wagner (Math. Ann., 114 (1937), pp. 570-590). This paper proves the same result without using Wagner's structure theorem or even planar embeddings. Given that there is no structure theorem for graphs with no $K_6$-minor, we argue that this proof suggests a possible approach for attacking the Hadwiger Conjecture.