Minimum K_2,3-saturated Graphs

TL;DR

This paper determines the minimum number of edges in a K_{2,3}-saturated graph with n vertices, establishing a precise formula for all n >= 5.

Contribution

It provides a exact value for sat(n, K_{2,3}) for all n >= 5, advancing the understanding of saturation numbers in graph theory.

Findings

Minimum edges in K_{2,3}-saturated graphs is 2n - 3 for n >= 5

Established the exact saturation number for all n >= 5

Contributed to extremal graph theory by solving a specific saturation problem.

Abstract

A graph is K_{2,3}-saturated if it has no subgraph isomorphic to K_{2,3}, but does contain a K_{2,3} after the addition of any new edge. We prove that the minimum number of edges in a K_{2,3}-saturated graph on n >= 5 vertices is sat(n, K_{2,3}) = 2n - 3.