Results 21 to 30 of about 29,700 (214)
On Colouring Point Visibility Graphs [PDF]
Discrete Applied Mathematics, 2017 In this paper we show that it can be decided in polynomial time whether or not the visibility graph of a given point set is 4-colourable, and such a 4-colouring, if it exists, can also be constructed in polynomial time. We show that the problem of deciding whether the visibility graph of a point set is 5-colourable, is NP-complete.
Bodhayan Roy, Ajit A. Diwan
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A reconfigurations analogue of Brooks’ theorem. [PDF]
, 2014 Let G be a simple undirected graph on n vertices with maximum degree Δ. Brooks’ Theorem states that G has a Δ-colouring unless G is a complete graph, or a cycle with an odd number of vertices. To recolour G is to obtain a new proper colouring by changing
A.E. Mouawad +15 more
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Colouring random graphs: Tame colourings
, 2023 75 pages.
Heckel, Annika, Panagiotou, Konstantinos
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The Complexity of 3-Colouring H-Colourable Graphs [PDF]
2019 IEEE 60th Annual Symposium on Foundations of Computer Science (FOCS), 2019 To appear in FOCS ...
Krokhin, A., Oprsal, J.
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On J-Colouring of Chithra Graphs [PDF]
National Academy Science Letters, 2020 The family of Chithra graphs is a wide ranging family of graphs which includes any graph of size at least one. Chithra graphs serve as a graph theoretical model for genetic engineering techniques or for modelling natural mutation within various biological networks found in living systems.
Sudev Naduvath, Johan Kok
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Complexity of colouring problems restricted to unichord-free and \{square,unichord\}-free graphs
, 2013 A \emph{unichord} in a graph is an edge that is the unique chord of a cycle. A \emph{square} is an induced cycle on four vertices. A graph is \emph{unichord-free} if none of its edges is a unichord.
de Figueiredo, Celina M. H. +2 more
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Certain Chromatic Sums of Some Cycle Related Graph Classes
, 2016 Let $\mathcal{C} = \{c_1,c_2, c_3, \ldots,c_k\}$ be a certain type of proper $k$-colouring of a given graph $G$ and $\theta(c_i)$ denote the number of times a particular colour $c_i$ is assigned to the vertices of $G$.
Chithra, K. P., Kok, Johan, Sudev, N. K.
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Progress on the adjacent vertex distinguishing edge colouring conjecture
, 2020 A proper edge colouring of a graph is adjacent vertex distinguishing if no two adjacent vertices see the same set of colours. Using a clever application of the Local Lemma, Hatami (2005) proved that every graph with maximum degree $\Delta$ and no ...
Joret, Gwenaël, Lochet, William
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Journal of Combinatorial Theory, Series B, 1982 An ordered colouring of a graph with k colours is a vertex colouring with colours {1, 2,…,k} such that each vertex coloured j is joined to at least one vertex-of colour i for each i less than j. Examples of ordered colourings are those produced by the greedy colouring algorithm.
Ernest J. Cockayne, Andrew Thomason
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Greedy Graph Colouring is a Misleading Heuristic [PDF]
, 2013 State of the art maximum clique algorithms use a greedy graph colouring as a bound. We show that greedy graph colouring can be misleading, which has implications for parallel branch and ...
McCreesh, Ciaran, Prosser, Patrick
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