A simple proof of Ore's theorem on the maximum size of k-connected graphs with given order and diameter

TL;DR

This paper provides a concise new proof of Ore's 1968 theorem that determines the maximum number of edges in a k-connected graph with specified order and diameter.

Contribution

It introduces a simplified proof of Ore's theorem, enhancing understanding and accessibility of this fundamental graph theory result.

Findings

New short proof of Ore's theorem

Clarifies the relationship between connectivity, size, and diameter

Simplifies the original proof for broader comprehension

Abstract

In 1968, Ore determined the maximum size of $k$-connected graphs with given order and diameter. In this note, we give a new short proof.