A generalization of Tur\'{a}n's theorem

TL;DR

This paper extends Turán's theorem, a fundamental result in extremal graph theory, providing a broader framework for understanding maximum edge counts in graphs avoiding certain subgraphs.

Contribution

It presents a generalized version of Turán's theorem, expanding its applicability and addressing a conjecture proposed by Balogh and Lidický.

Findings

Established a new generalized Turán's theorem

Confirmed the conjecture by Balogh and Lidický

Enhanced understanding of extremal graph structures

Abstract

We prove a generalization of Tur\'{a}n's theorem proposed by Balogh and Lidick\'{y}.