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Restricted Edge-colourings of Bipartite Graphs
Combinatorics, Probability and Computing, 1996Suppose each vertex of a bipartite multigraph (with partition (X, Y)) is assigned a set of colours; we say this colour scheme is feasible if the edges of the graph can be properly coloured so that each receives a colour in both of its endpoints' sets. We prove various results showing that certain types of colour scheme are always feasible. For instance,
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Matching, Edge-Colouring, and Dimers
2003We survey some recent results on finding and counting perfect matchings in regular bipartite graphs, with applications to bipartite edge-colouring and the dimer constant. Main results are improved complexity bounds for finding a perfect matching in a regular bipartite graph and for edge-colouring bipartite graphs, the solution of a problem of Erdős and
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The American Mathematical Monthly, 1972
(1972). An Edge-Colouring Problem. The American Mathematical Monthly: Vol. 79, No. 9, pp. 1018-1020.
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(1972). An Edge-Colouring Problem. The American Mathematical Monthly: Vol. 79, No. 9, pp. 1018-1020.
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Acyclic Edge Colouring of Outerplanar Graphs
2007An acyclicedge colouring of a graph is a proper edge colouring having no 2-coloured cycle, that is, a colouring in which the union of any two colour classes forms a linear forest. The acyclic chromatic indexof a graph is the minimum number ksuch that there is an acyclic edge colouring using kcolours and is usually denoted by ai¾?(G). Determining ai¾?(G)
Rahul Muthu +2 more
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The neighbour sum distinguishing relaxed edge colouring
Applied Mathematics and Computation, 2022Elżbieta Sidorowicz, Eric Duchêne
exaly
Strong edge-colouring of sparse planar graphs
Discrete Applied Mathematics, 2014Hervé Hocquard, Ararat Harutyunyan
exaly