Forbidden triples implying Hamiltonicity: for all graphs

Ralph J. Faudree; Ronald J. Gould; Michael S. Jacobson

Discussiones Mathematicae Graph Theory (2004)

  • Volume: 24, Issue: 1, page 47-54
  • ISSN: 2083-5892

Abstract

top
In [2], Brousek characterizes all triples of graphs, G₁, G₂, G₃, with G i = K 1 , 3 for some i = 1, 2, or 3, such that all G₁G₂G₃-free graphs contain a hamiltonian cycle. In [6], Faudree, Gould, Jacobson and Lesniak consider the problem of finding triples of graphs G₁, G₂, G₃, none of which is a K 1 , s , s ≥ 3 such that G₁, G₂, G₃-free graphs of sufficiently large order contain a hamiltonian cycle. In this paper, a characterization will be given of all triples G₁, G₂, G₃ with none being K 1 , 3 , such that all G₁G₂G₃-free graphs are hamiltonian. This result, together with the triples given by Brousek, completely characterize the forbidden triples G₁, G₂, G₃ such that all G₁G₂G₃-free graphs are hamiltonian.

How to cite

top

Ralph J. Faudree, Ronald J. Gould, and Michael S. Jacobson. "Forbidden triples implying Hamiltonicity: for all graphs." Discussiones Mathematicae Graph Theory 24.1 (2004): 47-54. <http://eudml.org/doc/270547>.

@article{RalphJ2004,
abstract = {In [2], Brousek characterizes all triples of graphs, G₁, G₂, G₃, with $G_i = K_\{1,3\}$ for some i = 1, 2, or 3, such that all G₁G₂G₃-free graphs contain a hamiltonian cycle. In [6], Faudree, Gould, Jacobson and Lesniak consider the problem of finding triples of graphs G₁, G₂, G₃, none of which is a $K_\{1,s\}$, s ≥ 3 such that G₁, G₂, G₃-free graphs of sufficiently large order contain a hamiltonian cycle. In this paper, a characterization will be given of all triples G₁, G₂, G₃ with none being $K_\{1,3\}$, such that all G₁G₂G₃-free graphs are hamiltonian. This result, together with the triples given by Brousek, completely characterize the forbidden triples G₁, G₂, G₃ such that all G₁G₂G₃-free graphs are hamiltonian.},
author = {Ralph J. Faudree, Ronald J. Gould, Michael S. Jacobson},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {hamiltonian; induced subgraph; forbidden subgraphs; Hamiltonian graph},
language = {eng},
number = {1},
pages = {47-54},
title = {Forbidden triples implying Hamiltonicity: for all graphs},
url = {http://eudml.org/doc/270547},
volume = {24},
year = {2004},
}

TY - JOUR
AU - Ralph J. Faudree
AU - Ronald J. Gould
AU - Michael S. Jacobson
TI - Forbidden triples implying Hamiltonicity: for all graphs
JO - Discussiones Mathematicae Graph Theory
PY - 2004
VL - 24
IS - 1
SP - 47
EP - 54
AB - In [2], Brousek characterizes all triples of graphs, G₁, G₂, G₃, with $G_i = K_{1,3}$ for some i = 1, 2, or 3, such that all G₁G₂G₃-free graphs contain a hamiltonian cycle. In [6], Faudree, Gould, Jacobson and Lesniak consider the problem of finding triples of graphs G₁, G₂, G₃, none of which is a $K_{1,s}$, s ≥ 3 such that G₁, G₂, G₃-free graphs of sufficiently large order contain a hamiltonian cycle. In this paper, a characterization will be given of all triples G₁, G₂, G₃ with none being $K_{1,3}$, such that all G₁G₂G₃-free graphs are hamiltonian. This result, together with the triples given by Brousek, completely characterize the forbidden triples G₁, G₂, G₃ such that all G₁G₂G₃-free graphs are hamiltonian.
LA - eng
KW - hamiltonian; induced subgraph; forbidden subgraphs; Hamiltonian graph
UR - http://eudml.org/doc/270547
ER -

References

top
  1. [1] P. Bedrossian, Forbidden Subgraph and Minimum Degree Conditions for Hamiltonicity (Ph.D. Thesis, Memphis State University, 1991). 
  2. [2] J. Brousek, Forbidden Triples and Hamiltonicity, Discrete Math. 251 (2002) 71-76, doi: 10.1016/S0012-365X(01)00326-0. Zbl1002.05044
  3. [3] G. Chartrand and L. Lesniak, Graphs & Digraphs (3rd Edition, Chapman & Hall, 1996). 
  4. [4] R.J. Faudree and R.J. Gould, Characterizing Forbidden Pairs for Hamiltonian Properties, Discrete Math. 173 (1997) 45-60, doi: 10.1016/S0012-365X(96)00147-1. Zbl0879.05050
  5. [5] R.J. Faudree, R.J. Gould and M.S. Jacobson, Potential Forbidden Triples Implying Hamiltonicity: For Sufficiently Large Graphs, preprint. Zbl1143.05051
  6. [6] R.J. Faudree, R.J. Gould, M.S. Jacobson and L. Lesniak, Characterizing Forbidden Clawless Triples for Hamiltonian Graphs, Discrete Math. 249 (2002) 71-81, doi: 10.1016/S0012-365X(01)00235-7. Zbl0990.05091

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.