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On k-intersection edge colourings

100%

Muthu R., Narayanan N., Subramanian C.

Discussiones Mathematicae Graph Theory

2009

tom 29

nr 2

411-418

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.

Oriented colouring of some graph products

100%

Aravind N., Narayanan N., Subramanian C.

Discussiones Mathematicae Graph Theory

2011

tom 31

nr 4

675-686

We obtain some improved upper and lower bounds on the oriented chromatic number for different classes of products of graphs.

Ograniczanie wyników

2 Discussiones Mathematicae Graph Theory

2 Narayanan N.

2 Subramanian C.

1 Aravind N.

1 Muthu R.

1 2011

1 2009

Wyniki wyszukiwania

On k-intersection edge colourings

Oriented colouring of some graph products