Generalized Majority Colourings of Digraphs
نویسندگان
چکیده
منابع مشابه
Majority Colourings of Digraphs
We prove that every digraph has a vertex 4-colouring such that for each vertex v, at most half the out-neighbours of v receive the same colour as v. We then obtain several results related to the conjecture obtained by replacing 4 by 3.
متن کاملOut-colourings of Digraphs
We study vertex colourings of digraphs so that no out-neighbourhood is monochromatic and call such a colouring an out-colouring. The problem of deciding whether a given digraph has an out-colouring with only two colours (called a 2-out-colouring) is NP-complete. We show that for every choice of positive integers r, k there exists a k-strong bipartite tournament which needs at least r colours in...
متن کاملMajority Choosability of Digraphs
A majority coloring of a digraph is a coloring of its vertices such that for each vertex v, at most half of the out-neighbors of v have the same color as v. A digraph D is majority k-choosable if for any assignment of lists of colors of size k to the vertices there is a majority coloring of D from these lists. We prove that every digraph is majority 4-choosable. This gives a positive answer to ...
متن کاملColourings, homomorphisms, and partitions of transitive digraphs
We investigate the complexity of generalizations of colourings (acyclic colourings, (k, `)colourings, homomorphisms, and matrix partitions), for the class of transitive digraphs. Even though transitive digraphs are nicely structured, many problems are intractable, and their complexity turns out to be difficult to classify. We present some motivational results and several open problems.
متن کاملOn path partitions and colourings in digraphs
We provide a new proof of a theorem of Saks which is an extension of Greene’s Theorem to acyclic digraphs, by reducing it to a similar, known extension of Greene and Kleitman’s Theorem. This suggests that the Greene-Kleitman Theorem is stronger than Greene’s Theorem on posets. We leave it as an open question whether the same holds for all digraphs, that is, does Berge’s conjecture concerning pa...
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ژورنال
عنوان ژورنال: Combinatorics, Probability and Computing
سال: 2017
ISSN: 0963-5483,1469-2163
DOI: 10.1017/s096354831700044x