On potentially $K_6-C_5$ graphic sequences

TL;DR

This paper characterizes the graphic sequences that can potentially realize a graph containing the specific subgraph $K_6 - C_5$, advancing understanding of subgraph realizability in degree sequences.

Contribution

It provides a complete characterization of potentially $K_6 - C_5$-graphic sequences, a specific class of subgraph-containing degree sequences.

Findings

Characterization of potentially $K_6 - C_5$-graphic sequences

Conditions for a degree sequence to realize a $K_6 - C_5$ subgraph

Extension of subgraph realization theory

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. In this paper, we characterize the potentially $K_6-C_5$ -graphic sequences.