Connected Even Factors in \(\{K_{1,\ell},K_{1,\ell}+e\}\) Free Graphs

Abstract

A connected factor \(F\) of a graph \(G\) is a connected spanning subgraph of \(G\). If the degree of each vertex in \(F\) is an even number between \(2\) and \(2s\), where \(s\) is an integer, then \(F\) is a connected even \([2, 2s]\)-factor of \(G\). In this paper, we prove that every supereulerian \(K_{1,\ell+1},K_{1,\ell+1}+e\)-free graph (\(\ell \geq 2\)) contains a connected even \([2, 2\ell – 2]\)-factor.