Karakterizacija ravninskih medianskih grafov

Median graphs have many interesting properties. One of them is-in connection with triangle free graphs-the recognition complexity. In general the complexity is not very fast, but if we restrict to the planar case the recognition complexity becomes linear. Despite this fact, there is no characterization of planar median graphs in the literature. Here an additional condition is introduced for the convex expansion procedure that characterizes planar median graphs.Medianski grafi imajo mnogo zanimivih lastnosti. Ena izmed njih je, v povezavi z grafi brez trikotnikov, je časovna zahtevnost za prepoznavanje teh grafov. V splošnem ta zahtevnost ni zelo hitra. Če pa se omejimo na ravninske medianske grafe, je časovna zahtevnost linearna. Kljub temu dejstvu v literaturi ne obstaja karakterizacija ravninskih medianskih grafov. V članku je predstavljen dodaten pogoj h konveksni ekspanziji, ki nam karakterizira ravninske medianske grafe