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379
Colouring random geometric graphs
"... some probability distribution ν on R d). For i � = j we join Xi and Xj by an edge if �Xi − Xj �< r(n). We study the properties of the chromatic number χn and clique number ωn of this graph as n becomes large, where we assume that r(n) → 0. We allow any choice ν that has a bounded density functio ..."
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Cited by 1 (1 self)
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some probability distribution ν on R d). For i � = j we join Xi and Xj by an edge if �Xi − Xj �< r(n). We study the properties of the chromatic number χn and clique number ωn of this graph as n becomes large, where we assume that r(n) → 0. We allow any choice ν that has a bounded density
5colouring graphs with 4 crossings ∗
, 2010
"... We disprove a conjecture of Oporowski and Zhao stating that every graph with crossing number at most 5 and clique number at most 5 is 5colourable. However, we show that every graph with crossing number at most 4 and clique number at most 5 is 5colourable. We also show some colourability results on ..."
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on graphs that can be made planar by removing few edges. In particular, we show that if a graph with clique number at most 5 has three edges whose removal leaves the graph planar, then it is 5colourable. 1
Edge Colouring Reduced Indifference Graphs
, 1999
"... The chromatic index problem  finding the minimum number of colours required for colouring the edges of a graph  is still unsolved for indifference graphs, whose vertices can be linearly ordered so that the vertices contained in the same maximal clique are consecutive in this order. Two adjacent ..."
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The chromatic index problem  finding the minimum number of colours required for colouring the edges of a graph  is still unsolved for indifference graphs, whose vertices can be linearly ordered so that the vertices contained in the same maximal clique are consecutive in this order. Two adjacent
Acyclic Colourings of 1Planar Graphs
, 2001
"... A graph is 1planar if it can be drawn on the plane in such a way that every edge crosses at most one other edge. We prove that the acyclic chromatic number of every 1planar graph is at most 20. ..."
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Cited by 11 (0 self)
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A graph is 1planar if it can be drawn on the plane in such a way that every edge crosses at most one other edge. We prove that the acyclic chromatic number of every 1planar graph is at most 20.
Interval Edge Colourings of Complete Graphs and ncubes
, 2007
"... For complete graphs and ncubes bounds are found for the possible number of colours in an interval edge colourings. Let G = (V, E) be an undirected graph without loops and multiple edges [1], V (G) and E(G) be the sets of vertices and edges of G, respectively. The degree of a vertex x ∈ V (G) is den ..."
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Cited by 1 (1 self)
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For complete graphs and ncubes bounds are found for the possible number of colours in an interval edge colourings. Let G = (V, E) be an undirected graph without loops and multiple edges [1], V (G) and E(G) be the sets of vertices and edges of G, respectively. The degree of a vertex x ∈ V (G
Graph homomorphisms, circular colouring, and fractional covering by hcuts
"... A graph homomorphism is a vertex map which carries edges from a source graph to edges in a target graph. The instances of the Weighted Maximum HColourable Subgraph problem (MAX HCOL) are edgeweighted graphs G and the objective is to find a subgraph of G that has maximal total edge weight, under t ..."
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Cited by 4 (3 self)
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A graph homomorphism is a vertex map which carries edges from a source graph to edges in a target graph. The instances of the Weighted Maximum HColourable Subgraph problem (MAX HCOL) are edgeweighted graphs G and the objective is to find a subgraph of G that has maximal total edge weight, under
List Edge Colourings of Some 1Factorable Multigraphs
, 1996
"... The List Edge Colouring Conjecture asserts that, given any multigraph G with chromatic index k and any set system fSe : e 2 E(G)g with each jSe j = k, we can choose elements se 2 Se such that se 6= sf whenever e and f are adjacent edges. Using a technique of Alon and Tarsi which involves the graph ..."
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Cited by 25 (0 self)
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The List Edge Colouring Conjecture asserts that, given any multigraph G with chromatic index k and any set system fSe : e 2 E(G)g with each jSe j = k, we can choose elements se 2 Se such that se 6= sf whenever e and f are adjacent edges. Using a technique of Alon and Tarsi which involves the graph
Bipartite edgecolouring in O(∆m) time
, 1996
"... We show that a minimum edgecolouring of a bipartite graph can be found in O(∆m) time, where ∆ and m denote the maximum degree and the number of edges of G, respectively. It is equivalent to finding a perfect matching in a kregular bipartite graph in O(km) time. By sharpening the methods, a minimu ..."
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Cited by 7 (1 self)
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We show that a minimum edgecolouring of a bipartite graph can be found in O(∆m) time, where ∆ and m denote the maximum degree and the number of edges of G, respectively. It is equivalent to finding a perfect matching in a kregular bipartite graph in O(km) time. By sharpening the methods, a
A computational analysis of colour constancy
 Oxford University
, 2003
"... 2 The visual stimulus associated with an object surface varies with the illumination falling on the object. Constancy of perceived surface colour under changing illumination implies that the illuminationdependent mapping from surface reflectance to stimulus is cancelled by a compensatory variation ..."
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Cited by 7 (0 self)
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retinal stimulus to perceived colour. Can this be doneand if so, what is the nature of the required compensatory mapping? We investigate this question for four quite different idealizations of the visual environment, discussing these in turn in the context of a very simple proposal about the nature
COLOURING LATTICE POINTS BY REAL NUMBERS
, 2005
"... Abstract. We establish a criterion for the existence of an fcolouring with a finite span of the ddimensional lattice graph Zd. Let G be an arbitrary connected simple graph. By d(u, v) we denote the graph distance between the vertices u, v of G. By a constraints function we mean any nonincreasing ..."
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Abstract. We establish a criterion for the existence of an fcolouring with a finite span of the ddimensional lattice graph Zd. Let G be an arbitrary connected simple graph. By d(u, v) we denote the graph distance between the vertices u, v of G. By a constraints function we mean any nonincreasing
Results 1  10
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379