Cactus Graphs and Graphs Complement Conjecture

TL;DR

This paper proves that all cactus graphs satisfy the graph complement conjecture by constructing an orthogonal representation of their complements in five-dimensional space.

Contribution

It provides a proof that cactus graphs meet the graph complement conjecture through explicit orthogonal representations.

Findings

Cactus graphs satisfy the graph complement conjecture.

Orthogonal representations of complements are constructed in b5=5 dimensions.

The proof confirms the conjecture for this class of graphs.

Abstract

In this paper we proof that any cactus graph satisfies graph complement conjecture by finding a orthogonal representation of its complement in $\mathbb{R}^5$.