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

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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 
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     title = {On distance local connectivity and vertex distance colouring},
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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/