Discussiones Mathematicae Graph Theory 29(2) (2009)
411418
doi: 10.7151/dmgt.1456
Rahul Muthu, N. Narayanan and C.R. Subramanian
The Institute of Mathematical Sciences
Taramani, Chennai600113, India
email: {rahulm,narayan,crs}@imsc.res.in

We show that f_{k}(Δ) = Θ([(Δ^{2})/k]). We also discuss some open problems.
Keywords: graph theory, kintersection edge colouring, probabilistic method.
2000 Mathematics Subject Classification: 05C15, 05D40.
[1]  N. Alon and B. Mohar, Chromatic number of graph powers, Combinatorics Probability and Computing 11 (2002) 110, doi: 10.1017/S0963548301004965. 
[2]  N. Alon and J. Spencer, The Probabilistic Method (John Wiley, 2000). 
[3]  A.C. Burris and R.H. Schelp, Vertexdistinguishing proper edge colourings, J. Graph Theory 26 (1997) 7082, doi: 10.1002/(SICI)10970118(199710)26:2<73::AIDJGT2>3.0.CO;2C. 
[4]  P. Erdös and L. Lovász, Problems and results on 3chromatic hypergraphs and some related questions, in: Infinite and Finite Sets, 1975. 
[5]  S.T. McCormick, Optimal approximation of sparse Hessians and its equivalence to a graph colouring problem, Mathematical Programming 26 (1983) 153171, doi: 10.1007/BF02592052. 
[6]  M. Molloy and B. Reed, Graph Coloring and the Probabilistic Method (Springer, Algorithms and Combinatorics, 2002). 
[7]  R. Motwani and P. Raghavan, Randomized Algorithms (Cambridge University Press, 1995). 
[8]  V.G. Vizing, On an estimate of the chromatic class of a pgraph, Metody Diskret. Analys. (1964) 2530. 
Received 3 December 2007
Revised 14 February 2009
Accepted 14 February 2009