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Highly edge‐connected factors using given lists on degrees
Author(s) -
Akbari Saieed,
Hasanvand Morteza,
Ozeki Kenta
Publication year - 2019
Publication title -
journal of graph theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 54
eISSN - 1097-0118
pISSN - 0364-9024
DOI - 10.1002/jgt.22373
Subject(s) - combinatorics , mathematics , enhanced data rates for gsm evolution , graph , factor (programming language) , vertex connectivity , discrete mathematics , computer science , vertex (graph theory) , artificial intelligence , programming language
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.