Results 41 to 50 of about 901,024 (319)
Colouring random graphs: Tame colourings
, 2023 75 pages.
Heckel, Annika, Panagiotou, Konstantinos
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Maximising ‐colourings of graphs
Journal of Graph Theory, 2019 AbstractFor graphs and , an ‐colouring of is a map such that . The number of ‐colourings of is denoted by . We prove the following: for all graphs and , there is a constant such that, if , the graph maximises the number of ‐colourings among all connected graphs with vertices and minimum degree . This answers a question of Engbers.
Hannah Guggiari, Alex Scott
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Efficacy of Cupping in the Treatment of Hypertension Disease Using Graph Colouring
Journal of Physics: Conference Series, 2019 Cupping therapy also well known as Hijama is an ancient and holistic method for treatment variety of infirmities particularly cardiovascular diseases such as hypertension.
M. A. Elizabeth +4 more
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Journal of Combinatorial Theory, Series B, 2012 27 pages, small revisions from previous version, this version appears in Journal of Combinatorial Theory Series ...
Engbers, John, Galvin, David
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Proper Rainbow Connection Number of Graphs
Discussiones Mathematicae Graph Theory, 2021 A path in an edge-coloured graph is called a rainbow path if its edges receive pairwise distinct colours. An edge-coloured graph is said to be rainbow connected if any two distinct vertices of the graph are connected by a rainbow path.
Doan Trung Duy, Schiermeyer Ingo
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Equitable colourings of Borel graphs
Forum of Mathematics, Pi, 2021 Hajnal and Szemerédi proved that if G is a finite graph with maximum degree $\Delta $ , then for every integer $k \geq \Delta +1$ , G has a proper colouring with k colours in which every two colour classes differ in size at most by $1$ ;
Anton Bernshteyn, Clinton T. Conley
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Note On The Game Colouring Number Of Powers Of Graphs
Discussiones Mathematicae Graph Theory, 2016 We generalize the methods of Esperet and Zhu [6] providing an upper bound for the game colouring number of squares of graphs to obtain upper bounds for the game colouring number of m-th powers of graphs, m ≥ 3, which rely on the maximum degree and the ...
Andres Stephan Dominique, Theuser Andrea
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Bipartite Ramsey numbers involving stars, stripes and trees
Electronic Journal of Graph Theory and Applications, 2013 The Ramsey number R(m, n) is the smallest integer p such that any blue-red colouring of the edges of the complete graph Kp forces the appearance of a blue Km or a red Kn.
Michalis Christou +2 more
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On kernels in strongly game-perfect digraphs and a characterisation of weakly game-perfect digraphs
AKCE International Journal of Graphs and Combinatorics, 2020 We prove that the game-perfect digraphs defined by Andres (2012) with regard to a digraph version of the maker-breaker graph colouring game introduced by Bodlaender (1991) always have a kernel.
Stephan Dominique Andres
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Improper colouring of (random) unit disk graphs [PDF]
Discrete Mathematics & Theoretical Computer Science, 2005 For any graph $G$, the $k$-improper chromatic number $χ ^k(G)$ is the smallest number of colours used in a colouring of $G$ such that each colour class induces a subgraph of maximum degree $k$.
Ross J. Kang +2 more
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