A Characterization On Potentially $K_6-C_4$-graphic Sequences

TL;DR

This paper characterizes the sequences of degrees that can be realized in a graph containing a specific subgraph, namely $K_6-C_4$, extending previous theorems in graph theory.

Contribution

It provides a complete characterization of potentially $K_6-C_4$-graphic sequences, advancing understanding of subgraph containment in degree sequences.

Findings

Characterization of potentially $K_6-C_4$-graphic sequences

Implication of the characterization on existing theorems

Extension of previous results by Hu and Lai

Abstract

For given a graph $H$, a graphic sequence $\pi=(d_1,d_2,...,d_n)$ is said to be potentially $H$-graphic if there exists a realization of $\pi$ containing $H$ as a subgraph. Let $K_m-H$ be the graph obtained from $K_m$ by removing the edges set $E(H)$ where $H$ is a subgraph of $K_m$. In this paper, we characterize the potentially $K_6-C_4$-graphic sequences. This characterization implies a theorem due to Hu and Lai [7].