Embedding graphs having Ore-degree at most five

TL;DR

This paper proves that large graphs with minimum degree at least two-thirds of the vertices contain all graphs with Ore-degree at most five, establishing a new embedding condition based on Ore-degree constraints.

Contribution

It introduces a novel embedding criterion for graphs with bounded Ore-degree into large graphs with high minimum degree.

Findings

Graphs with Ore-degree at most five are embeddable in large graphs with minimum degree at least 2n/3.

The result extends embedding theorems by incorporating Ore-degree constraints.

Provides a new perspective on graph embedding conditions based on Ore-degree.

Abstract

Let $H$ and $G$ be graphs on $n$ vertices, where $n$ is sufficiently large. We prove that if $H$ has Ore-degree at most 5 and $G$ has minimum degree at least $2n/3$ then $H\subset G.$