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DM

1998

1998

We consider edge-coloured multigraphs. A trail in such a multigraph is alternating if its successive edges diﬀer in colour. Let G be a 2-edge-coloured complete graph and let M be a 2-edge-coloured complete multigraph. M. Bankfalvi and Zs. Bankfalvi [2] obtained a necessary and suﬃcient condition for G to have a Hamiltonian alternating cycle. Generalizing this theorem, P. Das and S.B. Rao [7] characterized those G which contain a closed alternating trail visiting each vertex v in G exactly f(v) > 0 times. We solve the more general problem of determining the length of a longest closed alternating trail Tf visiting each vertex v in M at most f(v) > 0 times. Our result is a generalization of a theorem by R. Saad [18] that determines the length of a longest alternating cycle in G. We prove the existence of a polynomial algorithm for ﬁnding the desired trail Tf . In particular, this provides a solution to a question in [18].

Added |
22 Dec 2010 |

Updated |
22 Dec 2010 |

Type |
Journal |

Year |
1998 |

Where |
DM |

Authors |
Jørgen Bang-Jensen, Gregory Gutin |

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