Universality of Graphs with Few Triangles and Anti-Triangles

Dan Hefetz, Mykhaylo Tyomkyn

نتاج البحث: نشر في مجلةمقالةمراجعة النظراء

ملخص

We study 3-random-like graphs, that is, sequences of graphs in which the densities of triangles and anti-Triangles converge to 1/8. Since the random graph n,1/2 is, in particular, 3-random-like, this can be viewed as a weak version of quasi-randomness. We first show that 3-random-like graphs are 4-universal, that is, they contain induced copies of all 4-vertex graphs. This settles a question of Linial and Morgenstern [10]. We then show that for larger subgraphs, 3-random-like sequences demonstrate completely different behaviour. We prove that for every graph H on n ≥ 13 vertices there exist 3-random-like graphs without an induced copy of H. Moreover, we prove that for every â"" there are 3-random-like graphs which are â""-universal but not m-universal when m is sufficiently large compared to â"".

اللغة الأصليةالإنجليزيّة
الصفحات (من إلى)560-576
عدد الصفحات17
دوريةCombinatorics Probability and Computing
مستوى الصوت25
رقم الإصدار4
المعرِّفات الرقمية للأشياء
حالة النشرنُشِر - 1 يوليو 2016
منشور خارجيًانعم

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