Chromatic-index-critical graphs of orders 13 and 14
Bokal, Drago, 1978- ; Brinkmann, Gunnar ; Grünewald, Stefan
Graf je kritičen za barvanje povezav, če njegovih povezav ni mogoče pobarvati z ▫$\Delta$▫ barvami (▫$\Delta$▫ je maksimalna stopnja grafa), odstranitev poljubne povezave iz grafa pa zmanjša njegov ...kromatični indeks. Domneva o kritičnih grafih trdi, da je vsak tak graf lihega reda. Bila je ovržena; najmanjši znani protiprimer ima red 18. V članku pokažemo, da ne obstaja graf reda 14 kritičen za barvanje povezav. Skupaj z do sedaj znanimi rezultati to pove, da je 16 zadnji red, za katerega še lahko obstaja kritični graf. Izdelan je tudi celoten seznam vseh netrivialnih kritičnih grafov reda 13.
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