On k-intersection edge colourings

• Autorzy: Rahul Muthu , N. Narayanan , C.R. Subramanian
• Języki publikacji: EN

Abstrakty

EN

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
$fₖ(Δ) = max_{G : Δ(G) = Δ} {χ'ₖ(G)}$.
We show that fₖ(Δ) = Θ(Δ²/k). We also discuss some open problems.

Słowa kluczowe

EN

graph theory; k-intersection edge colouring; probabilistic method

Kategorie tematyczne

• 05C15: Coloring of graphs and hypergraphs
• 05D40: Probabilistic methods

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2009
• Tom: 29
• Numer: 2
• Strony: 411-418

Daty

wydano

2009

otrzymano

2007-12-03

poprawiono

2009-02-14

zaakceptowano

2009-02-14

Twórcy

autor

Rahul Muthu

• The Institute of Mathematical Sciences, Taramani, Chennai-600113, India

autor

N. Narayanan

• The Institute of Mathematical Sciences, Taramani, Chennai-600113, India

autor

C.R. Subramanian

• The Institute of Mathematical Sciences, Taramani, Chennai-600113, India

Bibliografia

• [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)26:2<73::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.

Identyfikatory

DOI

10.7151/dmgt.1456