Geodesic
On distance local connectivity and vertex distance colouring
Discussiones Mathematicae. Graph Theory, Tome 27 (2007) no. 2, pp. 209-227

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

In this paper, we give some sufficient conditions for distance local connectivity of a graph, and a degree condition for local connectivity of a k-connected graph with large diameter. We study some relationships between t-distance chromatic number and distance local connectivity of a graph and give an upper bound on the t-distance chromatic number of a k-connected graph with diameter d.
Keywords: degree condition, distance local connectivity, distance chromatic number 
Holub, Přemysl. On distance local connectivity and vertex distance colouring. Discussiones Mathematicae. Graph Theory, Tome 27 (2007) no. 2, pp. 209-227. http://geodesic.mathdoc.fr/item/DMGT_2007_27_2_a0/
@article{DMGT_2007_27_2_a0,
     author = {Holub, P\v{r}emysl},
     title = {On distance local connectivity and vertex distance colouring},
     journal = {Discussiones Mathematicae. Graph Theory},
     pages = {209--227},
     year = {2007},
     volume = {27},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DMGT_2007_27_2_a0/}
}
TY  - JOUR
AU  - Holub, Přemysl
TI  - On distance local connectivity and vertex distance colouring
JO  - Discussiones Mathematicae. Graph Theory
PY  - 2007
SP  - 209
EP  - 227
VL  - 27
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/DMGT_2007_27_2_a0/
LA  - en
ID  - DMGT_2007_27_2_a0
ER  - 
%0 Journal Article
%A Holub, Přemysl
%T On distance local connectivity and vertex distance colouring
%J Discussiones Mathematicae. Graph Theory
%D 2007
%P 209-227
%V 27
%N 2
%U http://geodesic.mathdoc.fr/item/DMGT_2007_27_2_a0/
%G en
%F DMGT_2007_27_2_a0

[1] P. Baldi, On a generalized family of colourings, Graphs Combin. 6 (1990) 95-110, doi: 10.1007/BF01787722.

[2] J.A. Bondy and U.S.R. Murty, Graph Theory with Applications (Macmillan, London and Elsevier, 1976).

[3] G. Chartrand and R.E. Pippert, Locally connected graphs, Cas. pro pestování matematiky 99 (1974) 158-163.

[4] A. Chen, A. Gyárfás and R.H. Schelp, Vertex coloring with a distance restriction, Discrete Math. 191 (1998) 83-90, doi: 10.1016/S0012-365X(98)00094-6.

[5] P. Holub and L. Xiong, On Distance local connectivity and the hamiltonian index, submitted to Discrete Math.

[6] S. Jendrol' and Z. Skupień, Local structures in plane maps and distance colourings, Discrete Math. 236 (2001) 167-177, doi: 10.1016/S0012-365X(00)00440-4.

[7] F. Kramer and H. Kramer, Un problème de coloration des sommets d'un graphe, C.R. Acad. Sci. Paris Sér. A-B 268 (1969) A46-A48.

[8] F. Kramer and H. Kramer H, On the generalized chromatic number, Ann. Discrete Math. 30 (1986) 275-284.

[9] T. Madaras and A. Marcinová, On the structural result on normal plane maps, Discuss. Math. Graph Theory 22 (2002) 293-303, doi: 10.7151/dmgt.1176.

[10] Z. Ryjácek, On a closure concept in claw-free graphs, J. Combin. Theory (B) 70 (1997) 217-224, doi: 10.1006/jctb.1996.1732.

[11] Z. Skupień, Some maximum multigraphs and edge/vertex distance colourings, Discuss. Math. Graph Theory 15 (1995) 89-106, doi: 10.7151/dmgt.1010.