Simplified constructions of almost peripheral graphs and improved embeddings into them
Klavžar, Sandi ...
Center in periferija grafa sta množici vozlišč z najmanjšo oz. največjo ekscentričnostjo. Graf je skoraj periferen (AP), če vsa njegova vozlišča, razen natanko enega, ležijo v periferiji. ▫$r$▫-AP ...indeks ▫${\rm AP}_{r}(G)$▫ grafa ▫$G$▫ je najmanjše število vozlišč, ki jih moramo dodati grafu ▫$G$▫, da dobino ▫$r$▫-AP graf, v katerem ▫$G$▫ leži kot porojeni podgraf. V tem članku so predstavljene poenostavljene konstrukcije AP grafov. Dokazano je, da če je ▫$r\ge 2$▫ in ▫$n\ge 2$▫, potem velja ▫$AP_r(K_n) \leq 4r-3$▫. Nadalje je dokazano, da če ▫$G$▫ ni polni graf in ima vsaj tri vozlišča, potem velja ▫$AP_r(G) \leq 4r-4$▫. Na ta način je izboljšana prej znana ocena ▫$AP_r(G) \leq 4r-2$▫.
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