Geodesic
On k-intersection edge colourings
Discussiones Mathematicae. Graph Theory, Tome 29 (2009) no. 2, pp. 411-418 Cet article a éte moissonné depuis la source Library of Science

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We propose the following problem. For some k ≥ 1, a graph G is to be properly edge coloured such that any two adjacent vertices share at most k colours. We call this the k-intersection edge colouring. The minimum number of colours sufficient to guarantee such a colouring is the k-intersection chromatic index and is denoted χ'ₖ(G). Let fₖ be defined by
Keywords: graph theory, k-intersection edge colouring, probabilistic method 
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Muthu, Rahul; Narayanan, N.; Subramanian, C. On k-intersection edge colourings. Discussiones Mathematicae. Graph Theory, Tome 29 (2009) no. 2, pp. 411-418. http://geodesic.mathdoc.fr/item/DMGT_2009_29_2_a14/

[1] N. Alon and B. Mohar, Chromatic number of graph powers, Combinatorics Probability and Computing 11 (2002) 1-10, doi: 10.1017/S0963548301004965.

[2] N. Alon and J. Spencer, The Probabilistic Method (John Wiley, 2000).

[3] A.C. Burris and R.H. Schelp, Vertex-distinguishing proper edge colourings, J. Graph Theory 26 (1997) 70-82, doi: 10.1002/(SICI)1097-0118(199710)26:273::AID-JGT2>3.0.CO;2-C

[4] P. Erdös and L. Lovász, Problems and results on 3-chromatic 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) 153-171, 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 p-graph, Metody Diskret. Analys. (1964) 25-30.