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Title: Perfect divisibility and 2‐divisibility
Abstract

A graphGis said to be 2‐divisible if for all (nonempty) induced subgraphsHofG,can be partitioned into two setssuch thatand. (Heredenotes the clique number ofG, the number of vertices in a largest clique ofG). A graphGis said to be perfectly divisible if for all induced subgraphsHofG,can be partitioned into two setssuch thatis perfect and. We prove that if a graph is‐free, then it is 2‐divisible. We also prove that if a graph is bull‐free and either odd‐hole‐free orP5‐free, then it is perfectly divisible.

 
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NSF-PAR ID:
10059931
Author(s) / Creator(s):
 ;  
Publisher / Repository:
Wiley Blackwell (John Wiley & Sons)
Date Published:
Journal Name:
Journal of Graph Theory
Volume:
90
Issue:
1
ISSN:
0364-9024
Page Range / eLocation ID:
p. 54-60
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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