Results 21 to 30 of about 4,256 (307)
Entire choosability of near-outerplane graphs [PDF]
, 2008 It is proved that if G is a plane embedding of a K4-minor-free graph with maximum degree Δ, then G is entirely 7-choosable if Δ≤4 and G is entirely (Δ+ 2)-choosable if Δ≥ 5; that is, if every vertex, edge and face of G is given a list of max{7,Δ+2 ...
Timothy J. Hetherington +2 more
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The achromatic number of K_{6} □ K_{7} is 18 [PDF]
Opuscula Mathematica, 2021 A vertex colouring \(f:V(G)\to C\) of a graph \(G\) is complete if for any two distinct colours \(c_1, c_2 \in C\) there is an edge \(\{v_1,v_2\}\in E(G)\) such that \(f(v_i)=c_i\), \(i=1,2\).
Mirko Horňák
doaj +1 more source
New graph colouring algorithm for resource allocation in large-scale wireless networks [PDF]
, 2014 The vertex-colouring problem is a well-known classical problem in graph theory in which a colour is assigned to each vertex of the graph such that no two adjacent vertices have the same colour.
Ali, Sinan Ghassan Abid +9 more
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NP-completeness and One Polynomial Subclass of the Two-Step Graph Colouring Problem
Моделирование и анализ информационных систем, 2019 In this paper, we study the two-step colouring problem for an undirected connected graph. It is required to colour the graph in a given number of colours in a way, when no pair of vertices has the same colour, if these vertices are at a distance of 1 or ...
Natalya Sergeevna Medvedeva +1 more
doaj +1 more source
The harmonious chromatic number of almost all trees [PDF]
, 1995 A harmonious colouring of a simple graph G is a proper vertex colouring such that each pair of colours appears together on at most one edge. The harmonious chromatic number h(G) is the least number of colours in such a colouring.For any positive integer ...
Edwards, Keith
core +1 more source
From light edges to strong edge-colouring of 1-planar graphs [PDF]
Discrete Mathematics & Theoretical Computer Science, 2020 A strong edge-colouring of an undirected graph $G$ is an edge-colouring where every two edges at distance at most~$2$ receive distinct colours. The strong chromatic index of $G$ is the least number of colours in a strong edge-colouring of $G$.
Julien Bensmail +3 more
doaj +1 more source
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 0001
openaire +4 more sources
Backbone colouring and algorithms for TDMA scheduling [PDF]
Discrete Mathematics & Theoretical Computer Science, 2019 We investigate graph colouring models for the purpose of optimizing TDMA link scheduling in Wireless Networks. Inspired by the BPRN-colouring model recently introduced by Rocha and Sasaki, we introduce a new colouring model, namely the BMRN-colouring ...
Julien Bensmail +4 more
doaj +1 more source
Guide to graph colouring [PDF]
, 2021 This unique textbook treats graph colouring as an algorithmic problem, with a strong emphasis on practical applications. The work describes and analyses some of the best-known algorithms for colouring graphs, focusing on: whether these heuristics ...
Lewis, R. M. R.
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Cop-width, flip-width and strong colouring numbers [PDF]
Discrete Mathematics & Theoretical Computer ScienceCop-width and flip-width are new families of graph parameters introduced by Toru\'nczyk (2023) that generalise treewidth, degeneracy, generalised colouring numbers, clique-width and twin-width.
Robert Hickingbotham
doaj +1 more source