311 KB24 KB200820252016Lindner, Charles CurtisLo Faro, GiovanniTripodi, Antoinetteštevilka:1letnik:10str. 19-29COBISSID:17732697ISSN:1855-3966URN:URN:NBN:SI:doc-124WZNBLenUniverza na Primorskem, Fakulteta za matematiko, naravoslovje in informacijske tehnologijeArs mathematica contemporaneamaksimalna pakiranja 6-ciklovmaksimalna pakiranja trojicmaximum packing with 6-cyclesmaximum packing with triplesSquashing maximum packings of 6-cycles into maximum packings of triples|A 6-cycle is said to be squashed if we identify a pair of opposite vertices and name one of them with the other (and thereby turning the 6-cycle into a pair of triples with a common vertex). The squashing problem for 6-cycle systems was introduced by C. C. Lindner, M. Meszka and A. Rosa and completely solved by determining the spectrum. In this paper, by employing PBD and GDD-constructions and filling techniques, we extend this result by squashing maximum packings of ?$K_n$? with 6-cycles into maximum packings of ?$K_n$? with triples. More specifically, we establish that for each ?$n \ge 6$?, there is a max packing of ?$K_n$? with 6-cycles that can be squashed into a maximum packing of ?$K_n$? with triples6-cikel imenujemo stisnjen, če identificiramo par nasprotnih vozlišč in damo enemu od njiju ime drugega (na ta način pretvorimo 6-cikel v par trojic s skupnim vozliščem). Problem stisnjenja sistemov 6-ciklov, ki so ga zastavili C. C. Lindner, M. Meszka in A. Rosa, je bil popolnoma rešen z določitvijo spektra. V tem članku posplošimo ta rezultat s pomočjo PBD in GDD-konstrukcij in tehnik zapolnitve, in stisnemo maksimalna pakiranja ?$K_n$? s 6-cikli v maksimalna pakiranja ?$K_n$? s trojicami. Natančneje: pokažemo, da za vsak ?$n \ge 6$? obstaja maksimalno pakiranje grafa ?$K_n$? s 6-cikli, ki ga lahko stisnemo v maksimalno pakiranje grafa ?$K_n$? s trojicamiTEXTznanstveno časopisjejournalsSlovenian National E-content AggregatorNational and University Library of SloveniaUniverza na Primorskem, Fakulteta za naravoslovje, matematiko in informacijske tehnologije