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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
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Vertex-colouring edge-weightings with two edge weights [PDF]
Discrete Mathematics & Theoretical Computer Science, 2012 Graphs and ...
Mahdad Khatirinejad +4 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
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On Supereulerian 2-Edge-Coloured Graphs [PDF]
Graphs and Combinatorics, 2021 A 2-edge-coloured graph $G$ is {\bf supereulerian} if $G$ contains a spanning closed trail in which the edges alternate in colours. An {\bf eulerian factor} of a 2-edge-coloured graph is a collection of vertex disjoint induced subgraphs which cover all the vertices of $G$ such that each of these subgraphs is supereulerian.
Jørgen Bang-Jensen +2 more
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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
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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
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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
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Proper Rainbow Connection Number of Graphs
Discussiones Mathematicae Graph Theory, 2021 A path in an edge-coloured graph is called a rainbow path if its edges receive pairwise distinct colours. An edge-coloured graph is said to be rainbow connected if any two distinct vertices of the graph are connected by a rainbow path.
Doan Trung Duy, Schiermeyer Ingo
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Asymptotically good edge correspondence colourings
Journal of Graph Theory, 2022 AbstractWe prove that every simple graph with maximum degree has edge correspondence number .
Michael Molloy, Luke Postle
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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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