Distance-constrained grid colouring
نویسندگان
چکیده
منابع مشابه
Constrained colouring and σ-hypergraphs
A constrained colouring or, more specifically, an (α, β)-colouring of a hypergraph H, is an assignment of colours to its vertices such that no edge of H contains less than α or more than β vertices with different colours. This notion, introduced by Bujtás and Tuza, generalises both classical hypergraph colourings and more general Voloshin colourings of hypergraphs. In fact, for r-uniform hyperg...
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In this paper, we give some sufficient conditions for distance local connectivity of a graph, and a degree condition for local connectivity of a k-connected graph with large diameter. We study some relationships between t-distance chromatic number and distance local connectivity of a graph and give an upper bound on the t-distance chromatic number of a k-connected graph with diameter d.
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Scheduling problems that involve distance constraint tasks with repetitive requests is becoming increasingly popular in real time systems. Timing constraints defined by periods of fixed lengths for each task enforce some frequency of task execution. Alternatively deadlines could be specified relatively to the finish time of the previous execution of the same task. Hence the scheduling algorithm...
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This project aims to solve the 17×17 4-colouring challenge first proposed by William Gasarch in late 2009. The challenge is to fill a 17×17 grid with four colours such that no rectangle within the grid has the same colour in all of its four corners. This is one of the few unsolved problems in grid-colouring, and it has been studied from several different perspectives since the challenge was mad...
متن کاملA survey on the distance-colouring of graphs
In 1969 we defined in [8] and [9] the chromatic number γ(p,G) relative to distance p of a graph G to be the minimum number of colours sufficing for colouring the vertices of G in such a way that any two vertices of G of distance not greater than p have distinct colours. We gave also a characterization of the graphs for which we have γ(p,G) = p + 1. The same result was found by F. Speranza in [1...
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ژورنال
عنوان ژورنال: Acta Universitatis Sapientiae, Informatica
سال: 2016
ISSN: 2066-7760
DOI: 10.1515/ausi-2016-0001