Kaio Ariel Silva Sá
Institute of Science and Technology (ICT), Federal University of the Jequinhonha and Mucuri Valleys, Diamantina, Brazil

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A generalization of a Turán’s theorem about maximum clique on graphs Douglas Frederico Guimarães Santiago; Anderson Luiz Pedrosa Porto; Kaio Ariel Silva Sá
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 10, No 2 (2022): Electronic Journal of Graph Theory and Applications
Publisher : GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/ejgta.2022.10.2.10

Abstract

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.