The graph theory general position problem on some interconnection networks
Manuel, Paul ; Klavžar, Sandi
Problem splošne lege v teoriji grafov je naslednji: za dani graf ▫$G$▫ določi največje število vozlišč, tako da nobena trojica ne leži na skupni geodetki. Ta grafovska invarianta se imenuje število ...splošne lege (na kratko gp-število) in označuje z ▫${\rm gp}(G)$▫. V tem članku je gp-število določeno za širok razred podgrafov neskončne rešetke in neskončne diagonalne rešetke. Za izpeljavo teh rezultatov so vpeljane monotono-geodetke označitve ter dokazana "Monotone Geodesic Lemma". Slednja je izpeljana s pomočjo Erdös-Szekeres izreka o monotonih zaporednjih. Omejeneno je gp-število tridimenzionalnih neskončnih rešetk. S pomočjo izometričnih pokritij s potmi je določeno tudi gp-število Benešovih omrežij.
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