Hamiltonicity in Partly claw-free graphs

Moncef Abbas; Zineb Benmeziane

Hamiltonicity in Partly claw-free graphs

Moncef Abbas; Zineb Benmeziane

RAIRO - Operations Research (2009)

Volume: 43, Issue: 1, page 103-113
ISSN: 0399-0559

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Abstract

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 Matthews and Sumner have proved in [10] that if G is a 2-connected claw-free graph of order n such that δ(G) ≥ (n-2)/3, then G is Hamiltonian. We say that a graph is almost claw-free if for every vertex v of G, 〈N(v)〉 is 2-dominated and the set A of centers of claws of G is an independent set. Broersma et al. [5] have proved that if G is a 2-connected almost claw-free graph of order n such that n such that δ(G) ≥ (n-2)/3, then G is Hamiltonian. We generalize these results by considering the graphs satisfying the following property: for every vertex v ∈ A, there exist exactly two vertices x and y of V such that N(v) ⊆ N[x] ∪ N[y]. We extend some other known results on claw-free graphs to this new class of graphs.

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Abbas, Moncef, and Benmeziane, Zineb. "Hamiltonicity in Partly claw-free graphs." RAIRO - Operations Research 43.1 (2009): 103-113. <http://eudml.org/doc/250663>.

@article{Abbas2009,
abstract = { Matthews and Sumner have proved in [10] that if G is a 2-connected claw-free graph of order n such that δ(G) ≥ (n-2)/3, then G is Hamiltonian. We say that a graph is almost claw-free if for every vertex v of G, 〈N(v)〉 is 2-dominated and the set A of centers of claws of G is an independent set. Broersma et al. [5] have proved that if G is a 2-connected almost claw-free graph of order n such that n such that δ(G) ≥ (n-2)/3, then G is Hamiltonian. We generalize these results by considering the graphs satisfying the following property: for every vertex v ∈ A, there exist exactly two vertices x and y of V such that N(v) ⊆ N[x] ∪ N[y]. We extend some other known results on claw-free graphs to this new class of graphs. },
author = {Abbas, Moncef, Benmeziane, Zineb},
journal = {RAIRO - Operations Research},
keywords = {Graph theory; claw-free graphs; almost claw-free graphs; Hamiltonicity; matching.; graph theory; almost claw-free graphs; hamiltonicity; matching},
language = {eng},
month = {1},
number = {1},
pages = {103-113},
publisher = {EDP Sciences},
title = {Hamiltonicity in Partly claw-free graphs},
url = {http://eudml.org/doc/250663},
volume = {43},
year = {2009},
}

TY - JOUR
AU - Abbas, Moncef
AU - Benmeziane, Zineb
TI - Hamiltonicity in Partly claw-free graphs
JO - RAIRO - Operations Research
DA - 2009/1//
PB - EDP Sciences
VL - 43
IS - 1
SP - 103
EP - 113
AB -  Matthews and Sumner have proved in [10] that if G is a 2-connected claw-free graph of order n such that δ(G) ≥ (n-2)/3, then G is Hamiltonian. We say that a graph is almost claw-free if for every vertex v of G, 〈N(v)〉 is 2-dominated and the set A of centers of claws of G is an independent set. Broersma et al. [5] have proved that if G is a 2-connected almost claw-free graph of order n such that n such that δ(G) ≥ (n-2)/3, then G is Hamiltonian. We generalize these results by considering the graphs satisfying the following property: for every vertex v ∈ A, there exist exactly two vertices x and y of V such that N(v) ⊆ N[x] ∪ N[y]. We extend some other known results on claw-free graphs to this new class of graphs.
LA - eng
KW - Graph theory; claw-free graphs; almost claw-free graphs; Hamiltonicity; matching.; graph theory; almost claw-free graphs; hamiltonicity; matching
UR - http://eudml.org/doc/250663
ER -

References

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