Displaying similar documents to “Achromatic number of K 5 × K n for small n ”

Multicoloured Hamilton cycles.

Albert, Michael, Frieze, Alan, Reed, Bruce (1995)

The Electronic Journal of Combinatorics [electronic only]

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On k-intersection edge colourings

Rahul Muthu, N. Narayanan, C.R. Subramanian (2009)

Discussiones Mathematicae Graph Theory

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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 f ₖ ( Δ ) = m a x G : Δ ( G ) = Δ χ ' ₖ ( G ) . We show that fₖ(Δ) = Θ(Δ²/k). We also discuss some open problems.

Point-distinguishing chromatic index of the union of paths

Xiang'en Chen (2014)

Czechoslovak Mathematical Journal

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Let G be a simple graph. For a general edge coloring of a graph G (i.e., not necessarily a proper edge coloring) and a vertex v of G , denote by S ( v ) the set (not a multiset) of colors used to color the edges incident to v . For a general edge coloring f of a graph G , if S ( u ) ≠ S ( v ) for any two different vertices u and v of G , then we say that f is a point-distinguishing general edge coloring of G . The minimum number of colors required for a point-distinguishing general edge coloring of G , denoted...