On extremal weighted digraphs with no heavy paths
نویسندگان
چکیده
Bollobás and Scott proved that if the weighted outdegree of every vertex of a weighted digraph is at least 1, then it contains a (directed) path of weight at least 1. In this note we characterize the extremal weighted digraphs with no heavy paths. Our result is an extension of a corresponding theorem of Bondy and Fan in weighted graphs. Besides, we give examples showing the invalidity of generalizing a result of Bondy and Fan on the existence of heavy paths connecting two given vertices in a 2-connected weighted graph to a 2-strongly-connected weighted digraph.
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ورودعنوان ژورنال:
- Discrete Mathematics
دوره 310 شماره
صفحات -
تاریخ انتشار 2010