Hadwigerjeva hipoteza trdi, da se da vsak graf, ki ne vsebuje polnega grafa ▫$K_k$▫ kot minorja, obarvati s ▫$k-1$▫ barvami. Domneva je dokazana za ▫$k \le 6$▫ in odprta za večje vrednosti. Ni znano ...niti to, če obstaja taka konstanta ▫$c$▫,da se da vsak graf brez minorja ▫$K_k$▫ obarvati s ▫$ck$▫ barvami. V članku je dokazano, da obstaja taka eksplicitna konstanta ▫$f(k)$▫, da lahko vozlišca vsakega grafa brez minorja ▫$K_k$▫ razbijemo na bloke ▫$V_1,...,V_{\lceil 15.5k \rceil}$▫, tako da ima vsaka komponenta podgrafa induciranega na ▫$V_i$▫ ▫($i \ge 1)$▫ kvečjemu ▫$f(k)$▫ vozlišč. Ta rezultat je posplošen na seznamska barvanja, kjer zahtevamo, da imajo enobarvne komponente kvečjemu ▫$f(k)$▫ vozlišč.
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