# A Best Possible Result for the Square of a 2-Block to be Hamiltonian

## TL;DR

This paper proves the optimal condition under which the square of a 2-block graph contains a Hamiltonian cycle passing through four specified vertices and edges, extending understanding of Hamiltonian properties in graph squares.

## Contribution

It establishes the best possible result for the existence of Hamiltonian cycles in the square of a 2-block graph with four specified vertices and edges.

## Key findings

- Existence of Hamiltonian cycle in G^2 passing through four specified edges
- Result is proven to be optimal
- Applicable to 2-block graphs of order greater than 3

## Abstract

It is shown that for any choice of four different vertices x_1,...,x_4 in a 2-block G of order p>3, there is a hamiltonian cycle in G^2 containing four different edges x_iy_i of E(G) for certain vertices y_i, i=1,2,3,4. This result is best possible.