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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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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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Connected greedy colourings of perfect graphs and other classes: the good, the bad and the ugly [PDF]
Discrete Mathematics & Theoretical Computer ScienceThe Grundy number of a graph is the maximum number of colours used by the "First-Fit" greedy colouring algorithm over all vertex orderings. Given a vertex ordering $\sigma= v_1,\dots,v_n$, the "First-Fit" greedy colouring algorithm ...
Laurent Beaudou +6 more
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List circular backbone colouring [PDF]
Discrete Mathematics & Theoretical Computer Science, 2014 A natural generalization of graph colouring involves taking colours from a metric space and insisting that the endpoints of an edge receive colours separated by a minimum distance dictated by properties of the edge.
Frederic Havet, Andrew D. King
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Bounds On Fuzzy Dominator Chromatic Number of Fuzzy Soft Bipartite Graphs
Ratio Mathematica, 2023 An FSG GS(T,V) fuzzy’s soft dominator colouring (FSDC) is a suitable Fuzzy Soft Colouring (FSC) where every node of a colour group is dominated by a vertex of GS(T,V).
Jahir Hussain R, Afya Farhana M
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Bilangan Kromatik Grap Commuting dan Non Commuting Grup Dihedral
Cauchy: Jurnal Matematika Murni dan Aplikasi, 2015 Commuting graph is a graph that has a set of points X and two different vertices to be connected directly if each commutative in G. Let G non abelian group and Z(G) is a center of G.
Handrini Rahayuningtyas +2 more
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The Balanced Decomposition Number of TK4 and Series-Parallel Graphs
Discussiones Mathematicae Graph Theory, 2013 A balanced colouring of a graph G is a colouring of some of the vertices of G with two colours, say red and blue, such that there is the same number of vertices in each colour. The balanced decomposition number f(G) of G is the minimum integer s with the
Fujita Shinya, Liu Henry
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Algorithms, 2018 A k-colouring of a graph G with colours 1 , 2 , … , k is canonical with respect to an ordering π = v 1 , v 2 , … , v n of the vertices of G if adjacent vertices are assigned different colours and, for 1 ≤ c ≤ k
Ruth Haas, Gary MacGillivray
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