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On stability of Hamilton‐connectedness under the 2‐closure in claw‐free graphs
Author(s) -
Ryjáček Zdeněk,
Vrána Petr
Publication year - 2011
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.20497
Subject(s) - social connectedness , mathematics , claw , combinatorics , conjecture , vertex (graph theory) , closure (psychology) , discrete mathematics , graph , mechanical engineering , psychology , economics , engineering , market economy , psychotherapist
We show that, in a claw‐free graph, Hamilton‐connectedness is preserved under the operation of local completion performed at a vertex with 2‐connected neighborhood. This result proves a conjecture by Bollobás et al. © 2010 Wiley Periodicals, Inc. J Graph Theory 66:137‐151, 2011