356 KB24 KB200820252019Allagan, Julian D.Voloshin, Vitalyštevilka:1letnik:16str. 173-182ISSN:1855-3966COBISSID_HOST:18704729URN:URN:NBN:SI:doc-7Z26HAOEenUniverza na Primorskem, Fakulteta za matematiko, naravoslovje in informacijske tehnologijeArs mathematica contemporanea2-drevo2-treemaksimalen zunanjeravninskimaximal outerplanarpartitionrazdelitevStirling numbersStirlingova številaF-WORM colorings of some 2-trees: partition vectors|Suppose ?$\mathscr{F} = \{F_1, \ldots, F_t\}$? is a collection of distinct subgraphs of a graph ?$G = (V, E)$?. An ?$\mathscr{F}$?-WORM coloring of ?$G$? is the coloring of its vertices such that no copy of each subgraph ?$F_i \in \mathscr{F}$? is monochrome or rainbow. This generalizes the notion of ?$F$?-WORM coloring that was introduced recently by W. Goddard et al. Congr. Numerantium 219, 161--173 (2014). A (restricted) partition vector ?$(\zeta_{\alpha}, \ldots, \zeta_{\beta})$? is a sequence whose terms ?$\zeta_r$? are the number of ?$\mathscr{F}$?-WORM colorings using exactly ?$r$? colors, with ?$\alpha \leq r \leq \beta$?. The partition vectors of complete graphs and those of some 2-trees are discussed. We show that, although 2-trees admit the same partition vector in classic proper vertex colorings which forbid monochrome ?$K_2$?, their partition vectors in ?$K_3$?-WORM colorings are differentNaj bo ?$\mathscr{F} = \{F_1, \ldots, F_t\}$? zbirka različnih podgrafov grafa ?$G = (V, E)$?. ?$\mathscr{F}$?-WORM barvanje grafa ?$G$? je takšno barvanje njegovih vozlišč, pri katerem nobena kopija nobenega od podgrafov ?$F_i \in \mathscr{F}$? ni ne enobarvna ne mavrična. To je posplošitev pojma ?$F$?-WORM barvanja, ki so ga nedavno vpeljali W. Goddard, K. Wash in H. Xu. (Omejen) razdelitveni vektor ?$(\zeta_{\alpha}, \ldots, \zeta_{\beta})$? je zaporedje, katerega členi ?$\zeta_r$? so števila ?$\mathscr{F}$?-WORM barvanj z natanko ?$r$? barvami, kjer je ?$\alpha \leq r \leq \beta$?. Obravnavamo razdelitvene vektorje polnih grafov in nekaterih 2-dreves. Pokažemo, da četudi 2-drevesa premorejo enake razdelitvene vektorje pri klasičnem pravilnem barvanju vozlišč, ki prepoveduje enobarvne ?$K_2$?, so njihovi razdelitveni vektorji v ?$K_3$?-WORM barvanju lahko različniTEXTznanstveno časopisjejournalsSlovenian National E-content AggregatorNational and University Library of SloveniaUniverza na Primorskem, Fakulteta za naravoslovje, matematiko in informacijske tehnologije