Properly coloured Hamiltonian paths in edge-coloured complete graphs
نویسندگان
چکیده
منابع مشابه
Properly Coloured Hamiltonian Paths in Edge-coloured Complete Graphs
We consider edge-coloured complete graphs. A path or cycle Q is called properly coloured (PC) if any two adjacent edges of Q differ in colour. Our note is inspired by the following conjecture by B. Bollobás and P. Erdős (1976) : if G is an edge-coloured complete graph on n vertices in which the maximum monochromatic degree of every vertex is less than bn/2c, then G contains a PC Hamiltonian cyc...
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Given a c-edge-coloured multigraph, a proper Hamiltonian path is a path that contains all the vertices of the multigraph such that no two adjacent edges have the same colour. In this work we establish sufficient conditions for an edge-coloured multigraph to guarantee the existence of a proper Hamiltonian path, involving various parameters as the number of edges, the number of colours, the rainb...
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A conjecture of Erdős, Gyárfás, and Pyber says that in any edge-colouring of a complete graph with r colours, it is possible to cover all the vertices with r vertexdisjoint monochromatic cycles. So far, this conjecture has been proven only for r = 2. In this paper we show that in fact this conjecture is false for all r ≥ 3. In contrast to this, we show that in any edge-colouring of a complete g...
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In this short note, we study pairwise edge-disjoint rainbow spanning trees in properly edge-coloured complete graphs, where a graph is rainbow if its edges have distinct colours. Brualdi and Hollingsworth conjectured that every Kn properly edge-coloured by n−1 colours has n/2 edge-disjoint rainbow spanning trees. Kaneko, Kano and Suzuki later suggested this should hold for every properly edge-c...
متن کاملAlternating Hamiltonian circuits in edge-coloured bipartite graphs
Hilton, A. J. W., Alternating Hamiltonian circuits in edge-coloured bipartite graphs, Discrete Applied Mathematics 35 (1992) 271-273. We show that if G = K,, is edge-coloured with t-12 colours so that the subgraph induced by the edges of each colour is regular of order 2n, then G has a Hamiltonian circuit in which adjacent edges have different colours. We also give a generalization of this resu...
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 1998
ISSN: 0166-218X
DOI: 10.1016/s0166-218x(97)00062-0