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doi:10.1016/j.ipl.2005.01.008 
Copyright © 2005 Elsevier B.V. All rights reserved.
Between 2- and 3-colorability
Vadim V. Lozin
Received 22 September 2004;
revised 20 January 2005.
Communicated by M. Yamashita.
Available online 19 February 2005.
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Abstract
The recognition of 3-colorable graphs is an NP-complete problem, while 2-colorable (i.e., bipartite) graphs can be recognized in polynomial time. To make the complexity gap more precise, we study intermediate graph classes and respective problems. This note proposes a conjecture that separates difficult instances of the problem from polynomially solvable ones and proves the “polynomial” part of the conjecture.
Keywords: 3-colorability; Polynomial-time algorithm; Hereditary class of graphs; Computational complexity
