A generalization of Turán's theorem

✍ Benny Sudakov; Tibor Szabó; H. Van Vu 📂 Article 📅 2005 🏛 John Wiley and Sons 🌐 English ⚖ 94 KB

## Abstract In this paper, we obtain an asymptotic generalization of Turán's theorem. We prove that if all the non‐trivial eigenvalues of a __d__‐regular graph __G__ on __n__ vertices are sufficiently small, then the largest __K__~__t__~‐free subgraph of __G__ contains approximately (__t__ − 2)/(__

A generalization of a theorem of Turán

✍ N. Sauer 📂 Article 📅 1971 🏛 Elsevier Science 🌐 English ⚖ 136 KB

A weighted generalization of Tur�n's the

A weighted generalization of Tur�n's theorem

✍ Bondy, J. A.; Tuza, Zs. 📂 Article 📅 1997 🏛 John Wiley and Sons 🌐 English ⚖ 114 KB 👁 2 views

We obtain a generalization of Turán's theorem for graphs whose edges are assigned integer weights. We also characterize the extremal graphs in certain cases.

Turán's Theorem and Maximal Degrees

✍ Béla Bollobás 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 89 KB

graphs of order n and size at least t r (n) that do not have a vertex x of maximal degree d x whose neighbours span at least t r&1 (d x )+1 edges. Furthermore, we show that, for every graph G of order n and size at least t r (n), the degree-greedy algorithm used by Bondy (1983, J. Combin. Theory Ser

Turán's theorem for k-graphs

✍ Joel Spencer 📂 Article 📅 1972 🏛 Elsevier Science 🌐 English ⚖ 288 KB

Turán's theorem and k-connected graphs

✍ Nicolas Bougard; Gwenaël Joret 📂 Article 📅 2008 🏛 John Wiley and Sons 🌐 English ⚖ 167 KB

## Abstract The minimum size of a __k__‐connected graph with given order and stability number is investigated. If no connectivity is required, the answer is given by Turán's Theorem. For connected graphs, the problem has been solved recently independently by Christophe et al., and by Gitler and Val