Existence of 4-factors in star-free graphs with edge-connectivity conditions

Abstract

Let t ≥ 3 be an integer. We show that every 2-edge-connected K 1 , t -free graph with minimum degree at least max { 2 t − 3 , ⌈ 3 t + 1 2 ⌉ } , as well as every 3-edge-connected K 1 , t -free graph with minimum degree at least ⌈ 3 t + 1 2 ⌉ , has a 4-factor.