Discussiones Mathematicae Graph Theory 27(2) (2007) 209-227
doi: 10.7151/dmgt.1356

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Premysl Holub

Department of Mathematics
University of West Bohemia and Institute for Theoretical
Computer Science (ITI), Charles University
Univerzitni 22, 306 14 Pilsen, Czech Republic
e-mail: holubpre@kma.zcu.cz


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.

2000 Mathematics Subject Classification: 05C15, 05C75.


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Received 15 September 2005
Revised 18 May 2007
Accepted 18 May 2007