Geodesic
Improved Sufficient Conditions for Hamiltonian Properties
Discussiones Mathematicae. Graph Theory, Tome 35 (2015) no. 2, pp. 329-334

Voir la notice de l'article provenant de la source Library of Science

In 1980 Bondy [2] proved that a (k+s)-connected graph of order n ≥ 3 is traceable (s = −1) or Hamiltonian (s = 0) or Hamiltonian-connected (s = 1) if the degree sum of every set of k+1 pairwise nonadjacent vertices is at least ((k+1)(n+s−1)+1)/2. It is shown in [1] that one can allow exceptional (k+1)-sets violating this condition and still implying the considered Hamiltonian property. In this note we generalize this result for s = −1 and s = 0 and graphs that fulfill a certain connectivity condition.
Keywords: Hamiltonian, traceable, Hamiltonian-connected 
@article{DMGT_2015_35_2_a10,
     author = {Bode, Jens-P. and Fricke, Anika and Kemnitz, Arnfried},
     title = {Improved {Sufficient} {Conditions} for {Hamiltonian} {Properties}},
     journal = {Discussiones Mathematicae. Graph Theory},
     pages = {329--334},
     publisher = {mathdoc},
     volume = {35},
     number = {2},
     year = {2015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DMGT_2015_35_2_a10/}
}
TY  - JOUR
AU  - Bode, Jens-P.
AU  - Fricke, Anika
AU  - Kemnitz, Arnfried
TI  - Improved Sufficient Conditions for Hamiltonian Properties
JO  - Discussiones Mathematicae. Graph Theory
PY  - 2015
SP  - 329
EP  - 334
VL  - 35
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DMGT_2015_35_2_a10/
LA  - en
ID  - DMGT_2015_35_2_a10
ER  - 
%0 Journal Article
%A Bode, Jens-P.
%A Fricke, Anika
%A Kemnitz, Arnfried
%T Improved Sufficient Conditions for Hamiltonian Properties
%J Discussiones Mathematicae. Graph Theory
%D 2015
%P 329-334
%V 35
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DMGT_2015_35_2_a10/
%G en
%F DMGT_2015_35_2_a10
Bode, Jens-P.; Fricke, Anika; Kemnitz, Arnfried. Improved Sufficient Conditions for Hamiltonian Properties. Discussiones Mathematicae. Graph Theory, Tome 35 (2015) no. 2, pp. 329-334. http://geodesic.mathdoc.fr/item/DMGT_2015_35_2_a10/