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Toughness and hamiltonicity in almost claw‐free graphs
Author(s) -
Broersma H.J.,
Ryjáček Z.,
Schiermeyer I.
Publication year - 1996
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(199604)21:4<431::aid-jgt9>3.0.co;2-q
Subject(s) - combinatorics , claw , mathematics , pancyclic graph , graph , discrete mathematics , chordal graph , 1 planar graph , mechanical engineering , engineering
Some known results on claw‐free ( K 1.3 ‐free) graphs are generalized to the larger class of almost claw‐free graphs which were introduced by Ryjáček. In particular, we show that a 2‐connected almost claw‐free graph is 1‐tough, and that a 2‐connected almost claw‐free graph on n vertices is hamiltonian if δ ≥ 1/3 ( n − 2), thereby (partly) generalizing results of Matthews and Sumner. Finally, we use a result of Bauer et al. to show that a 2‐connected almost claw‐free graph on n vertices is hamiltonian if d(u) + d(v) + d(w) ≥ n for all independent sets of vertices u, v, and w. © 1996 John Wiley & Sons, Inc.