# On embedding degree sequences

## TL;DR

This paper investigates conditions under which one graphic degree sequence can be embedded as a subgraph within any realization of another degree sequence, advancing understanding of graph embedding properties.

## Contribution

It introduces new criteria for embedding degree sequences, providing a deeper theoretical understanding of subgraph realizability within degree sequence constraints.

## Key findings

- Established sufficient conditions for degree sequence embedding
- Characterized when one degree sequence can always be realized as a subgraph
- Extended existing theories on graphic sequences and subgraph realizations

## Abstract

Assume that we are given two graphic sequences, $\pi_1$ and $\pi_2$. We consider conditions for $\pi_1$ and $\pi_2$ which guarantee that there exists a simple graph $G_2$ realizing $\pi_2$ such that $G_2$ is the subgraph of any simple graph $G_1$ that realizes $\pi_1$.