Edge-switching homomorphisms of edge-coloured graphs
نویسندگان
چکیده
منابع مشابه
Homomorphisms of Edge-coloured Graphs and Coxeter Groups
Let G1 = (V1, E1) and G2 = (V2, E2) be two edge-coloured graphs (without multiple edges or loops). A homomorphism is a mapping φ : V1 7−→ V2 for which, for every pair of adjacent vertices u and v of G1, φ(u) and φ(v) are adjacent in G2 and the colour of the edge φ(u)φ(v) is the same as that of the edge uv. We prove a number of results asserting the existence of a graph G, edge-coloured from a s...
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Graphs with m disjoint edge sets are considered, both in the presence of a switching operation and without one. The operation of switching at a vertex x with respect to a finite permutation group Γ involves using some group element to change the sets to which the edges incident with the vertex x belong. We show that some of the colouring theory developed for signed graphs, and for oriented grap...
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We consider homomorphisms and vertex colourings of m-edge-coloured graphs that have a switching operation which permutes the colours of the edges incident with a specified vertex. The permutations considered arise from the action of the symmetric, alternating and dihedral groups on the set of edge colours. In all cases, after studying the equivalence classes of medge-coloured graphs determined ...
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In this paper, we consider properly edge-coloured (PC) paths and cycles in edge-coloured graphs. We consider a family of transformations of an edge-coloured graph G into an ordinary graph that allow us to check the existence PC cycles and PC (s, t)-paths in G and, if they exist, to find shortest ones among them. We raise a problem of finding the optimal transformation and consider a possible so...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2009
ISSN: 0012-365X
DOI: 10.1016/j.disc.2008.03.021