Bounds On The Inducibility Of Double Loop Graphs

TL;DR

This paper establishes new upper bounds on the inducibility of double loop graphs, advancing understanding of extremal graph densities with near-optimal bounds for specific graph orders.

Contribution

It provides novel upper bounds for the inducibility of double loop graphs, including near-tight bounds for orders 5 and 6.

Findings

Upper bound for k=5 within 0.964506 factor of exact inducibility

Upper bound for k=6 within 3 times the best known lower bound

Advances extremal graph theory by refining inducibility bounds

Abstract

In the area of extremal graph theory, there exists a problem that investigates the maximum induced density of a $k$-vertex graph $H$ in any $n$-vertex graph $G$. This is known as the problem of \emph{inducibility} that was first introduced by Pippenger and Golumbic in 1975. In this paper, we give a new upper bound for the inducibility for a family of \emph{Double Loop Graphs} of order $k$. The upper bound obtained for order $k=5$ is within a factor of 0.964506 of the exact inducibility, and the upper bound obtained for $k=6$ is within a factor of 3 of the best known lower bound.