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A general position problem in graph theoryManuel, Paul ; Klavžar, SandiV klasičnem "no-three-in-line" problemu želimo poiskati največje število točk, ki jih lahko postavimo na ▫$n \times n$▫ mrežo, tako da nobene tri točke ne ležijo na skupni premici. Splošnejši problem ... za dano nmožico točk ▫$S$▫ v ravnini sprašuje, kolikšna je največja podmnožica točk ▫$S'$▫ od ▫$S$▫, tako da nobena trojica ni kolinearna. Motivirani s tema problemoma v tem članku vpeljemo naseldnjo grafovsko inačico problema. Za dani graf ▫$G$▫ določi največjo podmnožico vozlišč ▫$S$▫, tako da nobena trojica iz množice ▫$S$▫ ne leži na najkrajši poti v ▫$G$▫. Taki množici pravimo gp-množica grafa ▫$G$▫, njena velikost je gp-število ▫${\rm gp}(G)$▫ grafa ▫$G$▫. Dokazane so zgornje meje za ▫${\rm gp}(G)$▫ izražene z različnimi izometričnimi pokritji. Meje so uporabljene za določitev gp-števila različnih razredov grafov. Raziskovane so povezave med množicami vozlišč v splošni legi in pakiranji. Kot posledica so dokazane spodnje meje za gp-število. Dokazano je tudi, da je problem splošne lege NP-poln.Source: Bulletin of the Australian Mathematical Society. - ISSN 0004-9727 (Vol. 98, iss. 2, Oct. 2018, str. 177-187)Type of material - article, component part ; adult, seriousPublish date - 2018Language - englishCOBISS.SI-ID - 18443609
source: Bulletin of the Australian Mathematical Society. - ISSN 0004-9727 (Vol. 98, iss. 2, Oct. 2018, str. 177-187)
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Manuel, Paul | |
Klavžar, Sandi | 05949 |
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