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13.
Star chromatic index
Dvořák, Zdeněk ; Mohar, Bojan, 1956- ; Šámal, Robert
Zvezdni kromatični indeks grafa definiramo kot najmanjše možno število barv, s katerimi lahko pravilno obarvamo povezave grafa, tako da dobi vsaka pot ali cikel na štirih povezavah vsaj tri različne ...barve. Dokazana je "skoraj linearna" zgornja meja zvezdnega kromatičnega indeksa v odvisnosti od maksimalne stopnje grafa. Glede spodnje meje je za polne grafe reda ▫$n$▫ dokazana spodnja meja ▫$2n(1+o(1))$▫. Za primer kubičnih grafov pa je dokazano, da ima njihov zvezdni kromatični indeks vrednost med 4 in 7. Vsi grafi, kjer je dosežena spodnja meja 4 so karakterizirani. Dokazi temeljijo na različnih tehnikah iz drugih področij matematike in so zato še posebej zanimivi.
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