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Triangle‐free graphs that are signable without even holes
Author(s) -
Conforti Michele,
Cornuéjols Gérard,
Kapoor Ajai,
Vušković Kristina
Publication year - 2000
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 - 10.1002/1097-0118(200007)34:3<204::aid-jgt2>3.0.co;2-p
Subject(s) - mathematics , combinatorics , chordal graph , indifference graph , pathwidth , cograph , robertson–seymour theorem , 1 planar graph , discrete mathematics , split graph , class (philosophy) , clique sum , modular decomposition , graph , line graph , computer science , artificial intelligence
We characterize triangle‐free graphs for which there exists a subset of edges that intersects every chordless cycle in an odd number of edges (TF odd‐signable graphs). These graphs arise as building blocks of a decomposition theorem (for cap‐free odd‐signable graphs) obtained by the same authors. We give a polytime algorithm to test membership in this class. This algorithm is itself based on a decomposition theorem. © 2000 John Wiley & Sons, Inc. J Graph Theory 34: 204–220, 2000