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The general position achievement game played on graphs
Klavžar, Sandi ; Neethu, P. K. ; Ullas Chandran, S.V., 1984-
Množica v splošni legi grafa ▫$G$▫ je množica vozlišč ▫$S$▫ v ▫$G$▫, pri kateri nobena tri vozlišča iz ▫$S$▫ ne ležijo na skupni najkrajši poti. V tem članku vpeljemo in preučujemo igro doseganja za ...splošno lego. Igro na grafu ▫$G$▫ igrata igralca A in B, ki izmenično izbirata vozlišča grafa ▫$G$▫. Izbira vozlišča je legalna, če vozlišče še ni bilo izbrano in množica doslej izbranih vozlišč tvori množico v splošni legi. Igralec, ki izbere zadnje vozlišče, zmaga. Opisana so legalna vozlišča na vsakem koraku igre in podani so zadostni pogoji za zmago vsakega od igralcev. Igra je preučena na kartezičnih in leksikografskih produktih. Med drugim je dokazano, da A zmaga v igri na ▫$K_n\Box K_m$▫, če in samo če sta ▫$n$▫ in ▫$m$▫ liha, in da B zmaga v igri na ▫$G\circ K_n$▫, če in samo če B zmaga na ▫$G$▫, ali pa je ▫$n$▫ liha.
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