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Perfectly contractile diamond‐free graphs
Author(s) -
Rusu Irena
Publication year - 1999
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/(sici)1097-0118(199912)32:4<359::aid-jgt5>3.0.co;2-u
Subject(s) - combinatorics , conjecture , mathematics , diamond , graph , clique , chordal graph , strong perfect graph theorem , discrete mathematics , 1 planar graph , chemistry , organic chemistry
Everett et al. [Everett et al., Discr Math, 1997] conjectured that a graph with no odd hole and no stretcher is perfectly contractile, i.e., it can be reduced to a clique by successively contracting even pairs. We show that this conjecture is true for diamond‐free graphs, and propose a polynomial algorithm to perform the successive contractions. © 1999 John Wiley & Sons, Inc. J Graph Theory 32: 359–389, 1999