Short proofs on $k$-extendible graphs

TL;DR

This paper provides concise inductive proofs for two established results on $k$-extendible graphs, utilizing a property from prior research to simplify the proofs.

Contribution

It introduces shorter, inductive proofs for known theorems on $k$-extendible graphs, building on a key property from earlier work.

Findings

Short inductive proofs of two known results on $k$-extendible graphs

Utilization of a property from previous research to simplify proofs

Enhanced understanding of $k$-extendible graphs through simplified proofs

Abstract

In this note, we give short inductive proofs of two known results on $k$-extendible graphs based on a property proved in [Qinglin Yu, A note on $n$-extendable graphs. Journal of Graph Theory, 16:349-353, 1992].