Results 1 to 10 of about 2,701 (163)
Forbidden Structures for Planar Perfect Consecutively Colourable Graphs [PDF]
Discussiones Mathematicae Graph Theory, 2017 A consecutive colouring of a graph is a proper edge colouring with posi- tive integers in which the colours of edges incident with each vertex form an interval of integers.
Borowiecka-Olszewska Marta +1 more
doaj +4 more sources
On Vizing's edge colouring question
Journal of Combinatorial Theory Series B, 2023 Soon after his 1964 seminal paper on edge colouring, Vizing asked the following question: can an optimal edge colouring be reached from any given proper edge colouring through a series of Kempe changes? We answer this question in the affirmative for triangle-free graphs.
OSCAR Defrain +2 more
exaly +3 more sources
An edge colouring of multigraphs [PDF]
Computer Science Journal of Moldova, 2007 We consider a strict k-colouring of a multigraph G as a surjection f from the vertex set of G into a set of colours {1,2,…,k} such that, for every non-pendant vertex χ of G, there exist at least two edges incident to χ and coloured by the same colour ...
Mario Gionfriddo, Alberto Amato
doaj +3 more sources
Edge-colouring and total-colouring chordless graphs
Discrete Mathematics, 2013 A graph $G$ is \emph{chordless} if no cycle in $G$ has a chord. In the present work we investigate the chromatic index and total chromatic number of chordless graphs. We describe a known decomposition result for chordless graphs and use it to establish that every chordless graph of maximum degree $Δ\geq 3$ has chromatic index $Δ$ and total chromatic ...
Celina Miraglia Herrera de Figueiredo +2 more
exaly +5 more sources
Edge colouring by total labellings
Discrete Mathematics, 2010 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Michaell Stiebitz, Dieter Rautenbach
exaly +3 more sources
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
On \delta^(k)-colouring of Powers of Paths and Cycles
Theory and Applications of Graphs, 2021 In a proper vertex colouring of a graph, the vertices are coloured in such a way that no two adjacent vertices receive the same colour, whereas in an improper vertex colouring, adjacent vertices are permitted to receive same colours subjected to some ...
Merlin Ellumkalayil, Sudev Naduvath
doaj +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
Vertex-colouring edge-weightings with two edge weights [PDF]
Discrete Mathematics & Theoretical Computer Science, 2012 Graphs and ...
Mahdad Khatirinejad +4 more
doaj +1 more source
Visual‐attention GAN for interior sketch colourisation
IET Image Processing, 2021 In the professional field of interior designing, sketch colouring is often a time‐consuming and vapidity task. The traditional neural network does not handle the semantic relationship of sketch lines well, and the colouring effect is unsatisfactory. This
Xinrong Li +4 more
doaj +1 more source