On distance local connectivity and vertex distance colouring

Přemysl Holub

Discussiones Mathematicae Graph Theory (2007)

  • Volume: 27, Issue: 2, page 209-227
  • ISSN: 2083-5892

Abstract

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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.

How to cite

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Přemysl Holub. "On distance local connectivity and vertex distance colouring." Discussiones Mathematicae Graph Theory 27.2 (2007): 209-227. <http://eudml.org/doc/270169>.

@article{PřemyslHolub2007,
abstract = {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.},
author = {Přemysl Holub},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {degree condition; distance local connectivity; distance chromatic number},
language = {eng},
number = {2},
pages = {209-227},
title = {On distance local connectivity and vertex distance colouring},
url = {http://eudml.org/doc/270169},
volume = {27},
year = {2007},
}

TY - JOUR
AU - Přemysl Holub
TI - On distance local connectivity and vertex distance colouring
JO - Discussiones Mathematicae Graph Theory
PY - 2007
VL - 27
IS - 2
SP - 209
EP - 227
AB - 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.
LA - eng
KW - degree condition; distance local connectivity; distance chromatic number
UR - http://eudml.org/doc/270169
ER -

References

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  3. [3] G. Chartrand and R.E. Pippert, Locally connected graphs, Cas. pro pestování matematiky 99 (1974) 158-163. Zbl0278.05113
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  7. [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. Zbl0165.57302
  8. [8] F. Kramer and H. Kramer H, On the generalized chromatic number, Ann. Discrete Math. 30 (1986) 275-284. Zbl0601.05020
  9. [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. Zbl1027.05028
  10. [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. Zbl0872.05032
  11. [11] Z. Skupień, Some maximum multigraphs and edge/vertex distance colourings, Discuss. Math. Graph Theory 15 (1995) 89-106, doi: 10.7151/dmgt.1010. Zbl0833.05036

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