Highly edge‐connected factors using given lists on degrees

Let G be a 2 k ‐edge‐connected graph with k ≥ 0 and let L ( v ) ⊆ { k , … , d G ( v ) } for every v ∈ V ( G ) . A spanning subgraph F of G is called an L ‐ factor , ifd F ( v ) ∈ L ( v )for every v ∈ V ( G ) . In this article, we show that if| L ( v ) | ≥ ⌈d G ( v ) 2 ⌉ + 1 for every v ∈ V ( G ) , then G has a k ‐edge‐connected L ‐factor. We also show that if k ≥ 1 and L ( v ) = { ⌊d G ( v ) 2 ⌋ , … , ⌈d G ( v ) 2 ⌉ + k } for every v ∈ V ( G ) , then G has a k ‐edge‐connected L ‐factor.