A generalization of a Turán’s theorem about maximum clique on graphs

Douglas Frederico Guimarães Santiago, Anderson Luiz Pedrosa Porto, Kaio Ariel Silva Sá


One of the most important Turán’s theorems establishes an inequality between the maximum clique and the number of edges of a graph. Since 1941, this result has received much attention and many of the different proofs involve induction and a probability distribution. In this paper we detail finite procedures that gives a proof for the Turán’s Theorem. Among other things, we give a generalization of this result. Also we apply this results to a Nikiforov’s inequality between the spectral radius and the maximum clique of a graph.


maximum clique, spectral radius, Turan’s theorem, probability distribution

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DOI: http://dx.doi.org/10.5614/ejgta.2022.10.2.10


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