Results 11 to 20 of about 4,256 (307)
Colouring a graph frugally [PDF]
Combinatorica, 1997 Every graph with maximum degree \(\Delta\geq\Delta_0\) has a proper \((\Delta+1)\)-coloring in which every color class has at most \(\log^8\Delta\) elements in the neighborhood of any vertex. If \(\beta\geq 1\) and the maximum degree is \(\delta\geq\Delta_\beta\) then there is a \(\max((\beta+1)\Delta,e^3\Delta^{1+{1\over\beta}})\)-coloring in which ...
Hind, H., Molloy, M., Reed, B.
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On a graph colouring problem [PDF]
Discrete Mathematics, 1999 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Cochand, M., Karolyi, G.
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Graph colouring algorithms [PDF]
, 2015 This chapter presents an introduction to graph colouring algorithms. The focus is on vertex-colouring algorithms that work for general classes of graphs with worst-case performance guarantees in a sequential model of computation. The presentation aims to demonstrate the breadth of available techniques and is organized by algorithmic paradigm.
Husfeldt, Thore
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Anagram-Free Graph Colouring [PDF]
The Electronic Journal of Combinatorics, 2018 An anagram is a word of the form $WP$ where $W$ is a non-empty word and $P$ is a permutation of $W$. We study anagram-free graph colouring and give bounds on the chromatic number. Alon et al.[Random Structures & Algorithms 2002] asked whether anagram-free chromatic number is bounded by a function of the maximum degree.
Tim E. Wilson, David R. Wood
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Graph Colouring and Decomposition [PDF]
, 2023 In this thesis we consider two variants on graph colouring. The first variant, ℓ-vertex-ranking requires that the vertices in the graph are assigned integer colours such that any path of length at most ℓ has a unique maximum colour.
Javarsineh, Mehrnoosh
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Topics in graph colouring [PDF]
, 2023 In this thesis, we study two variants of graph (vertex) colourings: multicolouring and correspondence colouring. In ordinary graph colouring, each vertex receives a colour. Such a colouring is proper if adjacent vertices receive different colours.
Xu, Xinyi
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On graphs double-critical with respect to the colouring number [PDF]
Discrete Mathematics & Theoretical Computer Science, 2015 The colouring number col($G$) of a graph $G$ is the smallest integer $k$ for which there is an ordering of the vertices of $G$ such that when removing the vertices of $G$ in the specified order no vertex of degree more than $k-1$ in the remaining graph ...
Matthias Kriesell, Anders Pedersen
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On dynamic colouring of cartesian product of complete graph with some graphs
Journal of Taibah University for Science, 2020 A proper vertex colouring is called a 2-dynamic colouring, if for every vertex v with degree at least 2, the neighbours of v receive at least two colours. The smallest integer k such that G has a dynamic colouring with k colours denoted by $\chi _2(G) $.
K. Kaliraj +2 more
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On the Colourings of Graphs [PDF]
Canadian Mathematical Bulletin, 1961 A graph G is defined by a set V(G) of vertices, a set E(G) of edges, and a relation of incidence which associates with each edge two distinct vertices called its ends. We consider only the case in which V(G) and E(G) are both finite.An n-colouring of G is usually defined as a mapping f of V(G) into the set of integers { 1, 2,…, n} which maps the two ...
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alberto-santini/selective-graph-colouring 1.1 [PDF]
, 2017 Code, instances, and best known solutions for the Selective Graph Colouring ...
Alberto Santini
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