On distance local connectivity and vertex distance colouring

• Autorzy: Přemysl Holub
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

degree condition; distance local connectivity; distance chromatic number

Kategorie tematyczne

• 05C15: Coloring of graphs and hypergraphs
• 05C75: Structural characterization of families of graphs

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2007
• Tom: 27
• Numer: 2
• Strony: 209-227

Daty

wydano

2007

otrzymano

2005-09-15

poprawiono

2007-05-18

zaakceptowano

2007-05-18

Twórcy

autor

Přemysl Holub

• Department of Mathematics, University of West Bohemia and Institute for Theoretical, Computer Science (ITI), Charles University, Univerzitni 22, 306 14 Pilsen, Czech Republic

Bibliografia

• [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.

Identyfikatory

DOI

10.7151/dmgt.1356