Results 11 to 20 of about 2,800 (262)
Partitions and Edge Colourings of Multigraphs [PDF]
The Electronic Journal of Combinatorics, 2008 Erdős and Lovász conjectured in 1968 that for every graph $G$ with $\chi(G)>\omega(G)$ and any two integers $s,t\geq 2$ with $s+t=\chi(G)+1$, there is a partition $(S,T)$ of the vertex set $V(G)$ such that $\chi(G[S])\geq s$ and $\chi(G[T])\geq t$. Except for a few cases, this conjecture is still unsolved.
Alexandr V. Kostochka, Michael Stiebitz
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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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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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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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Acyclic, Star and Oriented Colourings of Graph Subdivisions [PDF]
Discrete Mathematics & Theoretical Computer Science, 2005 Let G be a graph with chromatic number χ (G). A vertex colouring of G is \emphacyclic if each bichromatic subgraph is a forest. A \emphstar colouring of G is an acyclic colouring in which each bichromatic subgraph is a star forest. Let χ _a(G) and χ _s(G)
David R. Wood
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Colouring edges with many colours in cycles
Journal of Combinatorial Theory, Series B, 2014 The arboricity of a graph G is the minimum number of colours needed to colour the edges of G so that every cycle gets at least two colours. Given a positive integer p, we define the generalized p-arboricity Arb_p(G) of a graph G as the minimum number of colours needed to colour the edges of a multigraph G in such a way that every cycle C gets at least ...
Jaroslav Nesetril +2 more
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On Small Balanceable, Strongly-Balanceable and Omnitonal Graphs
Discussiones Mathematicae Graph Theory, 2022 In Ramsey Theory for graphs we are given a graph G and we are required to find the least n0 such that, for any n ≥ n0, any red/blue colouring of the edges of Kn gives a subgraph G all of whose edges are blue or all are red.
Caro Yair, Lauri Josef, Zarb Christina
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On Supereulerian 2-Edge-Coloured Graphs [PDF]
Graphs and Combinatorics, 2021 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Jørgen Bang-Jensen +2 more
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Line game-perfect graphs [PDF]
Discrete Mathematics & Theoretical Computer ScienceThe $[X,Y]$-edge colouring game is played with a set of $k$ colours on a graph $G$ with initially uncoloured edges by two players, Alice (A) and Bob (B). The players move alternately. Player $X\in\{A,B\}$ has the first move. $Y\in\{A,B,-\}$.
Stephan Dominique Andres, Wai Lam Fong
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On k-intersection edge colourings
Discussiones Mathematicae Graph Theory, 2009 We propose the following problem. For some \(k\geq 1\), a graph \(G\) is to be properly edge coloured such that any two adjacent vertices share at most \(k\) colours. We call this the \(k\)-intersection edge colouring. The minimum number of colours sufficient to guarantee such a colouring is the \(k\)-intersection chromatic index and is denoted ...
Rahul Muthu +2 more
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