FUZZY VERTEX ORDER COLOURING
نویسندگان
چکیده
منابع مشابه
Vertex-Colouring Edge-Weightings
A weighting w of the edges of a graph G induces a colouring of the vertices of G where the colour of vertex v, denoted cv, is ∑ e3v w(e). We show that the edges of every graph that does not contain a component isomorphic to K2 can be weighted from the set {1, . . . , 30} such that in the resulting vertex-colouring of G, for every edge (u, v) of G, cu 6= cv.
متن کاملParity vertex colouring of graphs
A parity path in a vertex colouring of a graph is a path along which each colour is used an even number of times. Let χp(G) be the least number of colours in a proper vertex colouring of G having no parity path. It is proved that for any graph G we have the following tight bounds χ(G) ≤ χp(G) ≤ |V (G)| − α(G) + 1, where χ(G) and α(G) are the chromatic number and the independence number of G, re...
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For a family F of graphs and a nonnegative integer k, F + ke and F − ke, respectively, denote the families of graphs that can be obtained from F graphs by adding and deleting at most k edges, and F + kv denotes the family of graphs that can be made into F graphs by deleting at most k vertices. This paper is mainly concerned with the parameterized complexity of the vertex colouring problem on F ...
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Brooks’ Theorem [R. L. Brooks, On Colouring the Nodes of a Network, Proc. Cambridge Philos. Soc. 37:194-197, 1941] states that every graph G with maximum degree ∆, has a vertex-colouring with ∆ colours, unless G is a complete graph or an odd cycle, in which case ∆ + 1 colours are required. Lovász [L. Lovász, Three short proofs in graph theory, J. Combin. Theory Ser. 19:269-271, 1975] gives an a...
متن کاملStepwise Development of Distributed Vertex Colouring
Verifying distributed algorithms is non trivial. A promising methodology is based on the Event B language and the refinement process ([1]) : it consists in redeveloping the algorithms by targeting a collection of required properties, using the refinement of models which preserves the properties of an abstract one in concrete ones. This approach has already been followed by Abrial et al for thei...
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ژورنال
عنوان ژورنال: International Journal of Pure and Apllied Mathematics
سال: 2016
ISSN: 1311-8080,1314-3395
DOI: 10.12732/ijpam.v107i3.9