A Characterization On Potentially $K_{2,5}$-graphic Sequences

TL;DR

This paper characterizes the graphic sequences that can realize a graph containing a $K_{2,5}$ subgraph, extending understanding of graph realizations with specific subgraph structures.

Contribution

It provides a complete characterization of potentially $K_{2,5}$-graphic sequences, building on and extending previous theorems in the field.

Findings

Characterization of potentially $K_{2,5}$-graphic sequences

Implication of a special case of Yin et al.'s theorem

Extension of existing graph realization results

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 potentially $K_{2,5}$-graphic sequences. This characterization implies a special case of a theorem due to Yin et al. [26].