Tattooing and the Tattoo Number of Graphs
Johan Kok, Naduvath Sudev

TL;DR
This paper introduces the concept of tattooing in directed graphs, a novel variation of graph cleaning that involves coloring arcs with brushes and their blends, defining the tattoo number as a derivative of the brush number.
Contribution
It proposes a new graph parameter called the tattoo number, extending the brush number concept with coloring and blending of brushes in directed graphs.
Findings
Defined the tattooing process and tattoo number for directed graphs.
Established relationships between brush number and tattoo number.
Explored conditions for tattooing along out-arcs with color blends.
Abstract
Consider a network of pipes which have to be cleaned using some cleaning agents, called brushes, assigned to some vertices. The minimum number of brushes required for cleaning the network is called its brush number. The tattooing of a simple connected directed graph is a particular type of the cleaning in which an arc are coloured by the colour of the colour-brush transiting it and the tattoo number of is a corresponding derivative of brush numbers in it. Tattooing along an out-arc of a vertex may proceed if a minimum set of colour-brushes is allocated (primary colours) or combined with those which have arrived (including colour blends) together with mutation of permissible new colour blends, has cardinality greater than or equal to .
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Taxonomy
TopicsAdvanced Graph Theory Research · Limits and Structures in Graph Theory · Computational Geometry and Mesh Generation
