A note on hamiltonicity of generalized net-free graphs of large diameter

Authors:
Jan Brousek;Ralph J. Faudree;Zdenek Ryjácek
Affiliations:
Department of Mathematics, University of West Bohemia, P.O. Box 314 306 14 Pilsen, Czech Republic;Department of Mathematical Sciences, The University of Memphis, Memphis, TN;-
Venue:
Discrete Mathematics
Year:
2002

Citing 6
Cited 0

On a closure concept in claw-free graphs

Journal of Combinatorial Theory Series B
Characterizing forbidden pairs for hamiltonian properties

Discrete Mathematics
Minimal 2-connected non-hamiltonian claw-free graphs

Discrete Mathematics
Forbidden subgraphs, hamiltonicity and closure in claw-free graphs

Discrete Mathematics
Forbidden subgraphs, stability and hamiltonicity

Discrete Mathematics
Graph Theory With Applications

Graph Theory With Applications

Quantified Score

Hi-index	0.05

Visualization

Abstract

A generalized (i,j,k)-net Ni,j,k is the graph obtained by identifying each of the vertices of a triangle with an endvertex of one of three vertex-disjoint paths of lengths i,j,k. We prove that every 2-connected claw-free N1,2,j-free graph of diameter at least max{7,2,j} (j ≥ 2) is hamiltonian.