1. On extremal weighted digraphs with no heavy paths
- Author
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Li, Binlong and Zhang, Shenggui
- Subjects
- *
DIRECTED graphs , *EXTREMAL problems (Mathematics) , *PATHS & cycles in graph theory , *TOPOLOGICAL degree , *GRAPH connectivity , *COMBINATORICS - Abstract
Abstract: Bollobás and Scott proved that if the weighted outdegree of every vertex of an edge-weighted digraph is at least 1, then the digraph contains a (directed) path of weight at least 1. In this note we characterize the extremal weighted digraphs with no heavy paths. Our result extends a corresponding theorem of Bondy and Fan on weighted graphs. We also give examples to show that a result of Bondy and Fan on the existence of heavy paths connecting two given vertices in a 2-connected weighted graph does not extend to 2-connected weighted digraphs. [Copyright &y& Elsevier]
- Published
- 2010
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