Thomassen's Choosability Argument Revisited
2010 (English)In: SIAM Journal on Discrete Mathematics, ISSN 0895-4801, E-ISSN 1095-7146, Vol. 24, no 4, 1632-1637 p.Article in journal (Refereed) Published
Thomassen (J. Combin. Theory Ser. B, 62 (1994), pp. 180-181) proved that every planar graph is 5-choosable. This result was generalized by. Skrekovski (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.
Place, publisher, year, edition, pages
2010. Vol. 24, no 4, 1632-1637 p.
Graph coloring, graph minor, choosability, list coloring, Hadwiger Conjecture
Engineering and Technology
IdentifiersURN: urn:nbn:se:kth:diva-28904DOI: 10.1137/100796649ISI: 000285505800026ScopusID: 2-s2.0-79251578348OAI: oai:DiVA.org:kth-28904DiVA: diva2:414087
QC 201105012011-05-022011-01-242011-05-02Bibliographically approved